Large Language Model (LLM) training is increasingly concentrated in homogeneous datacenters, while private data and underutilized GPUs across universities, laboratories, and edge sites remain difficult to use. This extended abstract presents preliminary results from a geo-distributed LLM training prototype that treats networking constraints as first-order design concerns. The prototype connects three heterogeneous GPU sites via cloud-hosted parameter servers, outbound-only gRPC streams, two-stage delta compression (INT8 quantization + Huffman coding, achieving up to 4× payload reduction), and fault-tolerant rejoin. In real deployments, GPT-2 Medium pretraining achieves stable loss reduction and reaches the target loss 15.2% faster in wall-clock time than the best tested baseline; Llama3-1B pretraining remains stable under larger communication pressure; and cross-site latency traces reveal site-dependent WAN spikes of up to 200s. These results motivate adaptive networking support for synchronization, compression, placement, telemetry, and recovery in geo-distributed LLM training.

In pretraining data detection, the goal is to detect whether a given sentence is in the dataset used for training a Large Language Model LLM). Recent methods (such as Min-K % and Min-K%++) reveal that most training corpora are likely contaminated with both sensitive content and evaluation benchmarks, leading to inflated test set performance. These methods sometimes fail to detect samples from the pretraining data, primarily because they depend on statistics composed of causal token likelihoods. We introduce Infilling Score, a new test-statistic based on non-causal token likelihoods. Infilling Score can be computed for autoregressive models without re-training using Bayes rule. A naive application of Bayes rule scales linearly with the vocabulary size. However, we propose a ratio test-statistic whose computation is invariant to vocabulary size. Empirically, our method achieves a significant accuracy gain over state-of-the-art methods including Min-K%, and Min-K%++ on the WikiMIA benchmark across seven models with different parameter sizes. Further, we achieve higher AUC compared to reference-free methods on the challenging MIMIR benchmark. Finally, we create a benchmark dataset consisting of recent data sources published after the release of Llama-3; this benchmark provides a statistical baseline to indicate potential corpora used for Llama-3 training.

Generative models transform random noise into images, while their inversion aims to reconstruct structured noise for recovery and editing. This paper addresses two key tasks: (i) *inversion* and (ii) *editing* of real images using stochastic equivalents of rectified flow models (e.g., Flux). While Diffusion Models (DMs) dominate the field of generative modeling for images, their inversion suffers from faithfulness and editability challenges due to nonlinear drift and diffusion. Existing DM inversion methods require costly training of additional parameters or test-time optimization of latent variables. Rectified Flows (RFs) offer a promising alternative to DMs, yet their inversion remains underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator, and prove that the resulting vector field is equivalent to a rectified stochastic differential equation. We further extend our framework to design a stochastic sampler for Flux. Our method achieves state-of-the-art performance in zero-shot inversion and editing, surpassing prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference. See our project page https://rf-inversion.github.io/ for code and demo.

We propose Reference-Based Modulation (RB-Modulation), a new plug-and-play solution for training-free personalization of diffusion models. Existing training-free approaches exhibit difficulties in (a) style extraction from reference images in the absence of additional style or content text descriptions, (b) unwanted content leakage from reference style images, and (c) effective composition of style and content. RB-Modulation is built on a novel stochastic optimal controller where a style descriptor encodes the desired attributes through a terminal cost. The resulting drift not only overcomes the difficulties above, but also ensures high fidelity to the reference style and adheres to the given text prompt. We also introduce a cross-attention-based feature aggregation scheme that allows RB-Modulation to decouple content and style from the reference image. With theoretical justification and empirical evidence, our test-time optimization framework demonstrates precise extraction and control of *content* and *style* in a training-free manner. Further, our method allows a seamless composition of content and style, which marks a departure from the dependency on external adapters or ControlNets. See project page: https://rb-modulation.github.io/ for code and further details.

Machine unlearning algorithms aim to remove the influence of specific training samples, ideally recovering the model that would have resulted from training on the remaining data alone. We study unlearning in the overparameterized setting, where many models interpolate the data, and defining the solution as any loss minimizer over the retained set—as in prior work in the underparameterized setting—is inadequate, since the original model may already interpolate the retained data and satisfy this condition. In this regime, loss gradients vanish, rendering prior methods based on gradient perturbations ineffective, motivating both new unlearning definitions and algorithms. For this setting, we define the unlearning solution as the minimum-complexity interpolator over the retained data and propose a new algorithmic framework that only requires access to model gradients on the retained set at the original solution. We minimize a regularized objective over perturbations constrained to be orthogonal to these model gradients, a first-order relaxation of the interpolation condition. For different model classes, we provide exact and approximate unlearning guarantees and demonstrate that an implementation of our framework outperforms existing baselines across various unlearning experiments.

The power of foundation models (FMs) lies in their capacity to learn highly expressive representations that can be adapted to a broad spectrum of tasks. However, these pretrained models require additional training stages to become effective for downstream applications. In the multi-task setting, prior works have shown empirically that specific meta-learning approaches for preparing a model for future adaptation through parameter-efficient fine-tuning (PEFT) can outperform standard retraining methods, but the mechanism of the benefits of meta-learning has been largely unexplored. We introduce a framework for generic PEFT-based meta-learning to learn a model that can easily adapt to unseen tasks. For linear models using LoRA, we show that standard retraining is provably suboptimal for finding an adaptable set of parameters and provide strict performance guarantees for our proposed method. We verify these theoretical insights through experiments on synthetic data as well as real-data vision and language tasks. We observe significant performance benefits using a simple implementation of our proposed meta-learning scheme during retraining relative to the conventional approach.

Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by physics or nature. Consider, for example, generating electricity demand patterns with constraints on peak demand times. This can be used to stress-test the functioning of power grids during adverse weather conditions. Existing approaches for generating constrained time series are either not scalable or degrade sample quality. To address these challenges, we introduce Constrained Posterior Sampling (CPS), a diffusion-based sampling algorithm that aims to project the posterior mean estimate into the constraint set after each denoising update. Notably, CPS scales to a large number of constraints ($\sim100$) without requiring additional training. We provide theoretical justifications highlighting the impact of our projection step on sampling. Empirically, CPS outperforms state-of-the-art methods in sample quality and similarity to real time series by around 70\% and 22\%, respectively, on real-world stocks, traffic, and air quality datasets.

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both *likelihood modeling* and *generated text quality*. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the *Anchored Diffusion Language Model (ADLM)*, a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4\% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches. Please see our project page: [anchored-diffusion-llm.github.io](https://anchored-diffusion-llm.github.io/) for code and demo.

Sampling from the posterior distribution in latent diffusion models for inverse problems is computationally challenging. Existing methods often rely on Tweedie's first-order moments that tend to induce biased results [32]. Second-order approximations are computationally prohibitive, making standard reverse diffusion processes in-tractable for posterior sampling. We present Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler offering efficiency comparable to first-order Tweedie while enabling tractable reverse processes using second-order approximation. Theoretical results reveal that our approach establishes a lower bound through a surrogate loss and enables a tractable reverse process using the trace of the Hessian with only$\mathcal{O}(1)$compute. We show STSL out-performs SoTA solvers PSLD [43] and P2L [10] by reducing neural function evaluations by 4X and 8X, respectively, while enhancing sampling quality on FFHQ, ImageNet, and COCO benchmarks. Moreover, STSL extends to text-guided image editing, effectively mitigating residual distortions in corrupted images. To our best knowledge, this is the first work to offer an efficient second-order approximation for solving inverse problems using latent diffusion, which further enables editing real-world images with corruptions.

An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a *single* task or (ii) they are *linear*, very little is known about the closer-to-practice case of *nonlinear* NNs trained on *multiple* tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an $r$-dimensional subspace within the $d\gg r$-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of $d$. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all $r$ ground-truth features.

Cellular service providers (CSPs) require predicting the network performance for various reasons such as analyzing the impact of planned configuration changes and large-scale events on the network. Although network configurations are widely considered as key predictors of performance, we claim that they are insufficient for accurately predicting cellular network performance. The cellular networks are impacted by unmeasured external factors (e.g., weather, called latents), therefore, the performance prediction based solely on configurations may result in confounding effects. We show that the Mobility, Access, and Traffic (MAT) metrics should be considered in addition as network performance predictors. Using a large dataset collected from a live cellular network, we validate the claim and show the benefit of using MAT metrics for accurate performance prediction.

Cellular service providers (CSPs) aim to optimize network performance and enhance user experience by tuning network configurations. However, this process often requires continuous live network testing, which incurs significant operational costs. In this paper, we focus on predicting the impact of configuration changes using historical data, thereby reducing the need for live network tests. A key challenge in developing such a model is accounting for unobserved external factors (e.g., weather, referred to as latents) that can introduce confounding effects between configurations and performance metrics. To address this, we employ intermediate network metrics, called Mobility, Access, and Traffic (MAT) metrics, which are influenced by both configurations and latents, and in turn, affect performance metrics. We introduce Configuration Impact Prediction Analysis Toolkit (CIPAT), a novel two-stage toolkit developed using a comprehensive real-world dataset from live LTE networks. Our evaluation demonstrates that CIPAT enables CSPs to predict the performance impact of proposed configuration changes with up to 86% accuracy and 85% efficacy, thereby reducing the operational costs associated with configuration tuning.

A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with making a prediction in that context. As such, that learner must adapt to the context without additional training. We explore the role of *softmax* attention in an ICL setting where each context encodes a regression task. We show that an attention unit learns a window that it uses to implement a nearest-neighbors predictor adapted to the landscape of the pretraining tasks. Specifically, we show that this window widens with decreasing Lipschitzness and increasing label noise in the pretraining tasks. We also show that on low-rank, linear problems, the attention unit learns to project onto the appropriate subspace before inference. Further, we show that this adaptivity relies crucially on the softmax activation and thus cannot be replicated by the linear activation often studied in prior theoretical analyses.

This work considers the problem of finding a first-order stationary point of a non-convex function with potentially unbounded smoothness constant using a stochastic gradient oracle. We focus on the class of $(L_0,L_1)$-smooth functions proposed by Zhang et al. (ICLR’20). Empirical evidence suggests that these functions more closely capture practical machine learning problems as compared to the pervasive $L_0$-smoothness. This class is rich enough to include highly non-smooth functions, such as $\exp(L_1 x)$ which is $(0,\mathcal{O}(L_1))$-smooth. Despite the richness, an emerging line of works achieves the $\widetilde{\mathcal{O}}(\frac{1}{\sqrt{T}})$ rate of convergence when the noise of the stochastic gradients is deterministically and uniformly bounded. This noise restriction is not required in the $\L_0$-smooth setting, and in many practical settings is either not satisfied, or results in weaker convergence rates with respect to the noise scaling of the convergence rate.We develop a technique that allows us to prove $\mathcal{O}(\frac{\mathrm{poly}\log(T)}{\sqrt{T}})$ convergence rates for $(L_0,L_1)$-smooth functions without assuming uniform bounds on the noise support. The key innovation behind our results is a carefully constructed stopping time $\tau$ which is simultaneously “large” on average, yet also allows us to treat the adaptive step sizes before $\tau$ as (roughly) independent of the gradients. For general $(L_0,L_1)$-smooth functions, our analysis requires the mild restriction that the multiplicative noise parameter $\sigma_1 < 1$. For a broad subclass of $(L_0,L_1)$-smooth functions, our convergence rate continues to hold when $\sigma_1 \geq 1$. By contrast, we prove that many algorithms analyzed by prior works on $(L_0,L_1)$-smooth optimization diverge with constant probability even for smooth and strongly-convex functions when $\sigma_1 > 1$.

The goal of contrasting learning is to learn a representation that preserves underlying clusters by keeping samples with similar content, e.g. the “dogness” of a dog, close to each other in the space generated by the representation. A common and successful approach for tackling this unsupervised learning problem is minimizing the InfoNCE loss associated with the training samples, where each sample is associated with their augmentations (positive samples such as rotation, crop) and a batch of negative samples (unrelated samples). To the best of our knowledge, it was unanswered if the representation learned by minimizing the InfoNCE loss preserves the underlying data clusters, as it only promotes learning a representation that is faithful to augmentations, i.e., an image and its augmentations have the same representation. Our main result is to show that the representation learned by InfoNCE with a finite number of negative samples is also consistent with respect to {\em clusters} in the data, under the condition that the augmentation sets within clusters may be non-overlapping but are close and intertwined, relative to the complexity of the learning function class.

The use of alternate modalities, like images, for fast beamforming in the millimeter wave (mmWave)-band is being proposed to ensure high bandwidth connectivity in vehicular scenarios typically seen in the context of autonomous cars. Considering the dynamic deployment conditions, a car may encounter new environments which were not explicitly included in an apriori training dataset. In this paper, we propose to use the Model-Agnostic Meta-Learning (MAML) framework on the image data of the mmWave vehicle-to-infrastructure beam selection FLASH dataset, to overcome the generalization issues of a pre-trained model in unseen non-line-of-sight (NLOS) connectivity environments. MAML has additional advantages over traditional deep-learning techniques: (i) it uses a fraction of the data which, in turn, simplifies data collection and storage, and (ii) it results in equal or higher accuracy in optimal beam selection compared to the case when the new environment dataset is fully available during initial training. We show that our MAML implementation improves test accuracy of beam selection by up to 86% with fine-tuning when encountering an unseen NLOS environment compared to conventional supervised learning.

The study of collaborative multi-agent bandits has attracted significant attention recently. In light of this, we initiate the study of a new collaborative setting, consisting of $N$ agents such that each agent is learning one of $M$ stochastic multi-armed bandits to minimize their group cumulative regret. We develop decentralized algorithms which facilitate collaboration between the agents under two scenarios. We characterize the performance of these algorithms by deriving the per agent cumulative regret and group regret upper bounds. We also prove lower bounds for the group regret in this setting, which demonstrates the near-optimal behavior of the proposed algorithms.

Invariant representations are transformations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a *finite sample* setting, we consider the notion of $\epsilon$-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen intervened SEMs? Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds *probabilistically* over a family of linear SEMs without faithfulness assumptions.

We present the first framework to solve linear inverse problems leveraging pre-trained \textit{latent} diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to \textit{pixel-space} diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Cache management is critical for Content Delivery Networks (CDNs), impacting their performance and operational costs. Most production CDNs apply static, hand-tuned caching policy parameters at cache servers, such as admission frequency or size thresholds for the Hot Object Caches (HOC) of their system. However, these static policies fall short when a server is faced with unpredictable traffic pattern changes, even when policies employ multiple control parameters/knobs. Recent approaches have proposed learning-based solutions to dynamically adjust policy parameters, but they are limited in action space, caching objectives, or impose high overhead. We propose Darwin, a CDN cache management system that is robust to traffic pattern changes and can flexibly optimize different caching objectives with unrestricted action spaces. Darwin employs a three-stage pipeline involving traffic pattern feature collection, unsupervised clustering for classification, and neural bandit expert selection to choose the optimal caching policy. Through extensive simulations, experiments using an Apache Traffic Server (ATS)-based prototype, and theoretical analysis, we show that Darwin achieves significant performance gain w.r.t. different objectives such as maximizing object hit rates and minimizing disk writes, while simultaneously adapting to traffic pattern shifts. Darwin imposes negligible overhead and achieves high throughput compared to the state-of-the-art.

For the misspecified linear Markov decision process (MLMDP) model of Jin et al. [2020], we propose an algorithm with three desirable properties. (P1) Its regret after K episodes scales as Kmax{\ensuremath{\varepsilon}mis,\ensuremath{\varepsilon}tol}, where \ensuremath{\varepsilon}mis is the degree of misspecification and \ensuremath{\varepsilon}tol is a user-specified error tolerance. (P2) Its space and per-episode time complexities remain bounded as $K\rightarrow\infty$. (P3) It does not require \ensuremath{\varepsilon}mis as input. To our knowledge, this is the first algorithm satisfying all three properties. For concrete choices of \ensuremath{\varepsilon}tol, we also improve existing regret bounds (up to log factors) while achieving either (P2) or (P3) (existing algorithms satisfy neither). At a high level, our algorithm generalizes (to MLMDPs) and refines the Sup-Lin-UCB algorithm, which Takemura et al. [2021] recently showed satisfies (P3) in the contextual bandit setting. We also provide an intuitive interpretation of their result, which informs the design of our algorithm.

We study convergence rates of AdaGrad-Norm as an exemplar of adaptive stochastic gradient methods (SGD), where the step sizes change based on observed stochastic gradients, for minimizing non-convex, smooth objectives. Despite their popularity, the analysis of adaptive SGD lags behind that of non adaptive methods in this setting. Specifically, all prior works rely on some subset of the following assumptions: (i) uniformly-bounded gradient norms, (ii) uniformly-bounded stochastic gradient variance (or even noise support), (iii) conditional independence between the step size and stochastic gradient. In this work, we show that AdaGrad-Norm exhibits an order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}\right)$ after $T$ iterations under the same assumptions as optimally-tuned non adaptive SGD (unbounded gradient norms and affine noise variance scaling), and crucially, without needing any tuning parameters. We thus establish that adaptive gradient methods exhibit order-optimal convergence in much broader regimes than previously understood.

We study the problem of Gaussian bandits with general side information, as first introduced by Wu, Szepesvári, and György. In this setting, the play of an arm reveals information about other arms, according to an arbitrary a priori known side information matrix: each element of this matrix encodes the fidelity of the information that the “row" arm reveals about the “column" arm. In the case of Gaussian noise, this model subsumes standard bandits, full-feedback, and graph-structured feedback as special cases. In this work, we first construct an LP-based asymptotic instance-dependent lower bound on the regret. The LP optimizes the cost (regret) required to reliably estimate the suboptimality gap of each arm. This LP lower bound motivates our main contribution: the first known asymptotically optimal algorithm for this general setting.

Recent empirical evidence has driven conventional wisdom to believe that gradient-based meta-learning (GBML) methods perform well at few-shot learning because they learn an expressive data representation that is shared across tasks. However, the mechanics of GBML have remained largely mysterious from a theoretical perspective. In this paper, we prove that two well-known GBML methods, MAML and ANIL, as well as their first-order approximations, are capable of learning common representation among a set of given tasks. Specifically, in the well-known multi-task linear representation learning setting, they are able to recover the ground-truth representation at an exponentially fast rate. Moreover, our analysis illuminates that the driving force causing MAML and ANIL to recover the underlying representation is that they adapt the final layer of their model, which harnesses the underlying task diversity to improve the representation in all directions of interest. To the best of our knowledge, these are the first results to show that MAML and/or ANIL learn expressive representations and to rigorously explain why they do so.

We propose an algorithm that uses linear function approximation (LFA) for stochastic shortest path (SSP). Under minimal assumptions, it obtains sublinear regret, is computationally efficient, and uses stationary policies. To our knowledge, this is the first such algorithm in the LFA literature (for SSP or other formulations). Our algorithm is a special case of a more general one, which achieves regret square root in the number of episodes given access to a computation oracle.

We propose two linear bandits algorithms with per-step complexity sublinear in the number of arms $K$. The algorithms are designed for applications where the arm set is extremely large and slowly changing. Our key realization is that choosing an arm reduces to a maximum inner product search (MIPS) problem, which can be solved approximately without breaking regret guarantees. Existing approximate MIPS solvers run in sublinear time. We extend those solvers and present theoretical guarantees for online learning problems, where adaptivity (i.e., a later step depends on the feedback in previous steps) becomes a unique challenge. We then explicitly characterize the tradeoff between the per-step complexity and regret. For sufficiently large $K$, our algorithms have sublinear per-step complexity and $\widetilde O(\sqrt{T})$ regret. Empirically, we evaluate our proposed algorithms in a synthetic environment and a real-world online movie recommendation problem. Our proposed algorithms can deliver a more than 72 times speedup compared to the linear time baselines while retaining similar regret.

We propose and evaluate a learning-based framework to address multi-agent resource allocation in coupled wireless systems. In particular we consider, multiple agents (e.g., base stations, access points, etc.) that choose amongst a set of resource allocation options towards achieving their own performance objective /requirements, and where the performance observed at each agent is further coupled with the actions chosen by the other agents, e.g., through interference, channel leakage, etc. The challenge is to find the best collective action. To that end we propose a Multi-Armed Bandit (MAB) framework wherein the best actions (aka arms) are adaptively learned through online reward feedback. Our focus is on systems which are "weakly-coupled" wherein the best arm of each agent is invariant to others' arm selection the majority of the time - this majority structure enables one to develop light weight efficient algorithms. This structure is commonly found in many wireless settings such as channel selection and power control. We develop a bandit algorithm based on the Track-and-Stop strategy, which shows a logarithmic regret with respect to a genie. Finally through simulation, we exhibit the potential use of our model and algorithm in several wireless application scenarios.

The Federated Averaging (FedAvg) algorithm, which consists of alternating between a few local stochastic gradient updates at client nodes, followed by a model averaging update at the server, is perhaps the most commonly used method in Federated Learning. Notwithstanding its simplicity, several empirical studies have illustrated that the model output by FedAvg leads to a model that generalizes well to new unseen tasks after a few fine-tuning steps. This surprising performance of such a simple method, however, is not fully understood from a theoretical point of view. In this paper, we formally investigate this phenomenon in the multi-task linear regression setting. We show that the reason behind the generalizability of the FedAvg output is FedAvg’s power in learning the common data representation among the clients’ tasks, by leveraging the diversity among client data distributions via multiple local updates between communication rounds. We formally establish the iteration complexity required by the clients for proving such result in the setting where the underlying shared representation is a linear map. To the best of our knowledge, this is the first result showing that FedAvg learns an expressive representation in any setting. Moreover, we show that multiple local updates between communication rounds are necessary for representation learning, as distributed gradient methods that make only one local update between rounds provably cannot recover the ground-truth representation in the linear setting, and empirically yield neural network representations that generalize drastically worse to new clients than those learned by FedAvg trained on heterogeneous image classification datasets.

The stochastic multi-armed bandit setting has been recently studied in the non-stationary regime, where the mean payoff of each action is a non-decreasing function of the number of rounds passed since it was last played. This model captures natural behavioral aspects of the users which crucially determine the performance of recommendation platforms, ad placement systems, and more. Even assuming prior knowledge of the mean payoff functions, computing an optimal planning in the above model is NP-hard, while the state-of-the-art is a $1/4$-approximation algorithm for the case where at most one arm can be played per round. We first focus on the setting where the mean payoff functions are known. In this setting, we significantly improve the best-known guarantees for the planning problem by developing a polynomial-time $(1-{1}/{e})$-approximation algorithm (asymptotically and in expectation), based on a novel combination of randomized LP rounding and a time-correlated (interleaved) scheduling method. Furthermore, our algorithm achieves improved guarantees -- compared to prior work -- for the case where more than one arms can be played at each round. Moving to the bandit setting, when the mean payoff functions are initially unknown, we show how our algorithm can be transformed into a bandit algorithm with sublinear regret.

Cascading bandits is a natural and popular model that frames the task of learning to rank from Bernoulli click feedback in a bandit setting. For the case of unstructured rewards, we prove matching upper and lower bounds for the problem-independent (i.e., gap-free) regret, both of which strictly improve the best known. A key observation is that the hard instances of this problem are those with small mean rewards, i.e., the small click-through rates that are most relevant in practice. Based on this, and the fact that small mean implies small variance for Bernoullis, our key technical result shows that variance-aware confidence sets derived from the Bernstein and Chernoff bounds lead to optimal algorithms (up to log terms), whereas Hoeffding-based algorithms suffer order-wise suboptimal regret. This sharply contrasts with the standard (non-cascading) bandit setting, where the variance-aware algorithms only improve constants. In light of this and as an additional contribution, we propose a variance-aware algorithm for the structured case of linear rewards and show its regret strictly improves the state-of-the-art.

Current wireless networks employ sophisticated multi-user transmission techniques to fully utilize the physical layer resources for data transmission. At the MAC layer, these techniques rely on a semi-static map that translates the channel quality of users to the potential transmission rate (more precisely, a map from the Channel Quality Index to the Modulation and Coding Scheme) for user selection and scheduling decisions. However, such a static map does not adapt to the actual deployment scenario and can lead to large performance losses. Furthermore, adaptively learning this map can be inefficient, particularly when there are a large number of users. In this work, we make this learning efficient by clustering users. Specifically, we develop an online learning approach that jointly clusters users and channel-states, and learns the associated rate regions of each cluster. This approach generates a scenario-specific map that replaces the static map that is currently used in practice. Furthermore, we show that our learning algorithm achieves sub-linear regret when compared to an omniscient genie. Next, we develop a user selection algorithm for multi-user scheduling using the learned user-clusters and associated rate regions. Our algorithms are validated on the WiNGS simulator from AT&T Labs, that implements the PHY/MAC stack and simulates the channel. We show that our algorithm can efficiently learn user clusters and the rate regions associated with the user sets for any observed channel state. Moreover, our simulations show that a deployment-scenario-specific map significantly outperforms the current static map approach for resource allocation at the MAC layer.

In this paper, we study learning-assisted multi-user scheduling for the wireless downlink. There have been many scheduling algorithms developed that optimize for a plethora of performance metrics; however a systematic approach across diverse performance metrics and deployment scenarios is still lacking. We address this by developing a meta-scheduler – given a diverse collection of schedulers, we develop a learning-based overlay algorithm (meta-scheduler) that selects that “best” scheduler from amongst these for each deployment scenario. More formally, we develop a multi-armed bandit (MAB) framework for meta-scheduling that assigns and adapts a score for each scheduler to maximize reward (e.g., mean delay, timely throughput etc.). The meta-scheduler is based on a variant of the Upper Confidence Bound algorithm (UCB), but adapted to interrupt the queuing dynamics at the base-station so as to filter out schedulers that might render the system unstable. We show that the algorithm has a poly-logarithmic regret in the expected reward with respect to a genie that chooses the optimal scheduler for each scenario. Finally through simulation, we show that the meta-scheduler learns the choice of the scheduler to best adapt to the deployment scenario (e.g. load conditions, performance metrics).

We study a novel variant of the multi-armed bandit problem, where at each time step, the player observes an independently sampled context that determines the arms’ mean rewards. However, playing an arm blocks it (across all contexts) for a fixed number of future time steps. The above contextual setting captures important scenarios such as recommendation systems or ad placement with diverse users. This problem has been recently studied [Dickerson et al., AAAI 2018] in the full-information setting (i.e., assuming knowledge of the mean context-dependent arm rewards), where competitive ratio bounds have been derived. We focus on the bandit setting, where these means are initially unknown; we propose a UCB-based variant of the full-information algorithm that guarantees a $\mathcal{O}(\log T)$-regret w.r.t. an $\alpha$-optimal strategy in $T$ time steps, matching the $\Omega(\log(T))$ regret lower bound in this setting. Due to the time correlations caused by blocking, existing techniques for upper bounding regret fail. For proving our regret bounds, we introduce the novel concepts of delayed exploitation and opportunistic subsampling and combine them with ideas from combinatorial bandits and non-stationary Markov chains coupling.

Recent work has considered natural variations of the {\em multi-armed bandit} problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of {\em blocking bandits}, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms’ expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of absence of delays.

Deep neural networks have shown the ability to extract universal feature representations from data such as images and text that have been useful for a variety of learning tasks. However, the fruits of representation learning have yet to be fully-realized in federated settings. Although data in federated settings is often non-i.i.d. across clients, the success of centralized deep learning suggests that data often shares a global {\em feature representation}, while the statistical heterogeneity across clients or tasks is concentrated in the {\em labels}. Based on this intuition, we propose a novel federated learning framework and algorithm for learning a shared data representation across clients and unique local heads for each client. Our algorithm harnesses the distributed computational power across clients to perform many local-updates with respect to the low-dimensional local parameters for every update of the representation. We prove that this method obtains linear convergence to the ground-truth representation with near-optimal sample complexity in a linear setting, demonstrating that it can efficiently reduce the problem dimension for each client. Further, we provide extensive experimental results demonstrating the improvement of our method over alternative personalized federated learning approaches in heterogeneous settings.

In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as join-the-shortest-queue and shortest expected delay assume that the service rates and queue lengths of the servers are known to the dispatcher. In this work, we tackle the problem of job dispatching without the knowledge of service rates and queue lengths, where the dispatcher can only obtain noisy estimates of the service rates by observing job departures. This problem presents a novel exploration-exploitation trade-off between sending jobs to all the servers to estimate their service rates, and exploiting the currently known fastest servers to minimize the expected queueing delay. We propose a bandit-based exploration policy that learns the service rates from observed job departures. Unlike the standard multi-armed bandit problem where only one out of a finite set of actions is optimal, here the optimal policy requires identifying the optimal fraction of incoming jobs to be sent to each server. We present a regret analysis and simulations to demonstrate the effectiveness of the proposed bandit-based exploration policy.

Recent works have shown that agents facing independent instances of a stochastic K-armed bandit can collaborate to decrease regret. However, these works assume that each agent always recommends their individual best-arm estimates to other agents, which is unrealistic in envisioned applications (machine faults in distributed computing or spam in social recommendation systems). Hence, we generalize the setting to include n honest and m malicious agents who recommend best-arm estimates and arbitrary arms, respectively. We first show that even with a single malicious agent, existing collaboration-based algorithms fail to improve regret guarantees over a single-agent baseline. We propose a scheme where honest agents learn who is malicious and dynamically reduce communication with (i.e., "block") them. We show that collaboration indeed decreases regret for this algorithm, assuming m is small compared to K but without assumptions on malicious agents' behavior, thus ensuring that our algorithm is robust against any malicious recommendation strategy.

Millimeter-wave (mmWave) communications, using directional beams, is a key enabler for high-throughput mobile ad hoc networks. These directional beams are organized into multiple codebooks according to beam resolution, with each codebook consisting of a set of equal-width beams that cover the whole angular space. The code-book with narrow beams delivers high throughput, at the expense of scanning time. Therefore overall throughput maximization is achieved by selecting a mmWave codebook that balances between beamwidth (beamforming gain) and beam alignment overhead. Further, these codebooks have some potential natural structures such as the non-decreasing instantaneous rate or the unimodal throughput as one traverses from the codebook with wide beams to the one with narrow beams. We study the codebook selection problem through a multi-armed bandit (MAB) formulation in mmWave networks with rapidly-varying channels. We develop multiple novel Thompson Sampling-based algorithms for our setting given different codebook structures with theoretical guarantees on regret. We further collect real-world (60 GHz) measurements with 12-antenna phased arrays, and show the performance benefits of our approaches in an IEEE 802.11ad/ay emulation setting.

In TD-learning, off-policy sampling is known to be more practical than on-policy sampling, and by decoupling learning from data collection, it enables data reuse. It is known that policy evaluation has the interpretation of solving a generalized Bellman equation. In this paper, we derive finite-sample bounds for any general off-policy TD-like stochastic approximation algorithm that solves for the fixed-point of this generalized Bellman operator. Our key step is to show that the generalized Bellman operator is simultaneously a contraction mapping with respect to a weighted $\ell_p$-norm for each $p$ in $[1,\infty)$, with a common contraction factor. Off-policy TD-learning is known to suffer from high variance due to the product of importance sampling ratios. A number of algorithms (e.g. $Q^\pi(\lambda)$, Tree-Backup$(\lambda)$, Retrace$(\lambda)$, and $Q$-trace) have been proposed in the literature to address this issue. Our results immediately imply finite-sample bounds of these algorithms. In particular, we provide first-known finite-sample guarantees for $Q^\pi(\lambda)$, Tree-Backup$(\lambda)$, and Retrace$(\lambda)$, and improve the best known bounds of $Q$-trace in \citep{chen2021finite}. Moreover, we show the bias-variance trade-offs in each of these algorithms.

We propose an online algorithm for clustering channel-states and learning the associated achievable multiuser rates. Our motivation stems from the complexity of multiuser scheduling. For instance, MU-MIMO scheduling involves the selection of a user subset and associated rate selection each time-slot for varying channel states (the vector of quantized channels matrices for each of the users) — a complex integer optimization problem that is different for each channel state. Instead, our algorithm clusters the collection of channel states to a much lower dimension, and for each cluster provides achievable multiuser capacity trade-offs, which can be used for user and rate selection. Our algorithm uses a bandit approach, where it learns both the unknown partitions of the channel-state space (channel-state clustering) as well as the rate region for each cluster along a pre-specified set of directions, by observing the success/failure of the scheduling decisions (e.g. through packet loss). We propose an epoch-greedy learning algorithm that achieves a sub-linear regret, given access to a class of classifying functions over the channel-state space. We empirically validate our approach on a high-fidelity 5G New Radio (NR) wireless simulator developed within AT&T Labs. We show that our epoch-greedy bandit algorithm learns the channel-state clusters and the associated rate regions. Further, adaptive scheduling using this learned rate-region model (map from channel-state to the set of feasible rates) outperforms the corresponding hand-tuned static maps in multiple settings. Thus, we believe that auto-tuning cellular systems through learning-assisted scheduling algorithms can significantly improve performance in real deployments.

We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent’s regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.

Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show its finite-sample error bounds while using different stepsizes. The idea is to construct a smooth Lyapunov function using the generalized Moreau envelope, and show that the iterates of SA have negative drift with respect to that Lyapunov function. Our result is applicable in Reinforcement Learning (RL). In particular, we use it to establish the first-known convergence rate of the V-trace algorithm for off-policy TD-learning [18]. Importantly, our construction results in only a logarithmic dependence of the convergence bound on the size of the state-space.

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically equivalent across meta-training and meta-testing, rather than considering worst-case task performance. In this work we introduce the notion of ``task-robustness'' by reformulating the popular Model-Agnostic Meta-Learning (MAML) objective \citep{finn2017model} such that the goal is to minimize the maximum loss over the observed meta-training tasks. The solution to this novel formulation is task-robust in the sense that it places equal importance on even the most difficult and/or rare tasks. This also means that it performs well over all distributions of the observed tasks, making it robust to shifts in the task distribution between meta-training and meta-testing. We present an algorithm to solve the proposed min-max problem, and show that it converges to an $\epsilon$-accurate point at the optimal rate of $\mathcal{O}(1/\epsilon^2)$ in the convex setting and to an $(\epsilon, \delta)$-stationary point at the rate of $\mathcal{O}(\max\{1/\epsilon^5, 1/\delta^5\})$ in nonconvex settings. We also provide an upper bound on the new task generalization error that captures the advantage of minimizing the worst-case task loss, and demonstrate this advantage in sinusoid regression and image classification experiments.

We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. The distribution shift is due, in part, to \emph{unobserved} features in the datasets. The objective, then, is to find the best mixture distribution over the training datasets (with only observed features) such that training a learning algorithm using this mixture has the best validation performance. Our proposed algorithm, \textsf{Mix&amp;Match}, combines stochastic gradient descent (SGD) with optimistic tree search and model re-use (evolving partially trained models with samples from different mixture distributions) over the space of mixtures, for this task. We prove a novel high probability bound on the final SGD iterate without relying on a global gradient norm bound, and use it to show the advantages of model re-use. Additionally, we provide simple regret guarantees for our algorithm with respect to recovering the optimal mixture, given a total budget of SGD evaluations. Finally, we validate our algorithm on two real-world datasets.

We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the latent variable. To efficiently compute common entropy, we propose an iterative algorithm that can be used to discover the trade-off between the entropy of the latent variable and the conditional mutual information of the observed variables. We show two applications of common entropy in causal inference: First, under the assumption that there are no low-entropy mediators, it can be used to distinguish direct causation from spurious correlation among almost all joint distributions on simple causal graphs with two observed variables. Second, common entropy can be used to improve constraint-based methods such as PC or FCI algorithms in the small-sample regime, where these methods are known to struggle. We propose a modification to these constraint-based methods to assess if a separating set found by these algorithms are valid using common entropy. We finally evaluate our algorithms on synthetic and real data to establish their performance.

We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we combine structured state-space exploration through hierarchical partitioning with querying these partitions at multiple fidelities, and develop a multi-fidelity bandit based tree-search algorithm for noisy black-box optimization. We derive simple regret guarantees for our algorithm and validate its performance on real and synthetic datasets.

We study an online and streaming unsupervised classification system. Our setting consists of a collection of classifiers (with unknown confusion matrices) each of which can classify one sample per unit time, and which are accessed by a stream of unlabeled samples. Each sample is dispatched to one or more classifiers, and depending on the labels collected from these classifiers, may be sent to other classifiers to collect additional labels. The labels are continually aggregated. Once the aggregated label has high enough accuracy (a pre-specified threshold for accuracy) or the sample is sent to all the classifiers, the now labeled sample is ejected from the system. For any given pre-specified threshold for accuracy, the objective is to sustain the maximum possible rate of arrival of new samples, such that the number of samples in memory does not grow unbounded. In this paper, we characterize the Pareto-optimal region of accuracy and arrival rate, and develop an algorithm that can operate at any point within this region. Our algorithm uses queueing-based routing and scheduling approaches combined with novel online tensor decomposition method to learn the hidden parameters, to Pareto-optimality guarantees. We finally verify our theoretical results through simulations on two ensembles formed using AlexNet, VGG, and ResNet deep image classifiers.

We consider the wireless scheduling problem of jointly activating/de-activating base-stations and (opportunistically) scheduling from among the active base stations. Such systems are of increasing relevance in emerging wireless networks with dense overlapping coverage, where it suffices for only a (time-varying) subset of the base-stations to be active at any given time to satisfy traffic demands. In addition to queue stability (to ensure that traffic demands are met), we focus on optimizing for costs arising due to activating base-stations (switching base-station state between active/inactive), and maintaining activation (these costs arising due to energy consumption).We propose two algorithms-LASS-Static and LASS-Dynamic (LASS: Learning Aided Switching and Scheduling), both of which are explore-exploit policies for base-station switching and channel scheduling. In our setting, the switching action consists of two key decisions: when to switch, and what base-station activation state to switch to. Both LASS-Static and LASS-Dynamic determine the resulting switching state (i.e. `what to switch to as well as the schedule using current queue-lengths and (estimated) channel states. The crucial difference is in `when to switch'-LASS-Static determines these statically (motivated by an epsilon-greedy bandit approach), whereas LASS-Dynamic does so using current queue-lengths (thus correlating switching times, switching states and schedules). For either algorithm, existing Lyapunov-based techniques fail to establish stability, as the switching state dynamics correlate the base-station activation decisions with the channel evolution over time. Using novel drift based techniques, in this paper we derive stability, and provide explicit bounds on the expected cost and queue lengths for both algorithms. Furthermore, we show that adaptively selecting switching times in LASS-Dynamic results in an improved upper-tail of queue lengths compared to LASS-Static.

In this paper we propose an online algorithm for clustering channel-states and learning the associated achievable multiuser rates. Our motivation stems from the complexity of multiuser scheduling. For instance, MU-MIMO scheduling involves the selection of a user subset and associated rate selection each time-slot for varying channel states (the vector of quantized channels matrices for each of the users) - a complex integer optimization problem that is different for each channel state. Instead, our algorithm clusters the collection of channel states to a much lower dimension, and for each cluster provides achievable multiuser capacity trade-offs, which can be used for user and rate selection. Our algorithm uses a bandit approach, where it learns both the unknown partitions of the channel-state space (channel-state clustering) as well as the capacity region for each cluster along a pre-specified set of directions, by observing the success/failure of the scheduling decisions (e.g. through packet loss). We propose an epoch-greedy learning algorithm that achieves a sub-linear regret, given access to a class of classifying functions over the channel-state space. Finally, we empirically validate the performance of our algorithm through simulations.

Designing efficient and robust beam alignment strategies for millimeter wave (mmWave) systems is important for overcoming training overheads and practical hardware impairments. In this work, we leverage side information in the form of prior knowledge of the angular support of the propagation channel (direction information) to design a compressive sensing (CS) based beam alignment algorithm. Existing CS based channel estimation approaches assume perfect phase information of the measurements, which is not the case with the low-cost off-the-shelf mmWave phased arrays. Instead, we develop a two-stage algorithm where we use the magnitude of measurements (aka non-coherent measurements); using phase retrieval (PR) followed by sparse recovery, we estimate the channel gain across various (quantized) spatial angles. To validate the proposed algorithm, we develop a fully reconfigurable mmWave testbed with custom-made 2-bit phased arrays. We perform a careful calibration to the phased arrays, thus enabling generations of precise desired beam patterns. Our implementation and real experiments validate both the proposed algorithm and calibration process by demonstrating consistency between the experimental results and the theoretical analysis.

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same product recommendation repeatedly) or infeasible (e.g. compute job scheduling on machines). We show that with prior knowledge of the rewards and delays of all the arms, the problem of optimizing cumulative reward does not admit any pseudo-polynomial time algorithm (in the number of arms) unless randomized exponential time hypothesis is false, by mapping to the PINWHEEL scheduling problem. Subsequently, we show that a simple greedy algorithm that plays the available arm with the highest reward is asymptotically $(1-1/e)$ optimal. When the rewards are unknown, we design a UCB based algorithm which is shown to have $c \log T + o(\log T)$ cumulative regret against the greedy algorithm, leveraging the free exploration of arms due to the unavailability. Finally, when all the delays are equal the problem reduces to Combinatorial Semi-bandits providing us with a lower bound of $c' \log T+ \omega(\log T)$.

We consider the problem of contextual bandits with stochastic experts, which is a variation of the traditional stochastic contextual bandit with experts problem. In our problem setting, we assume access to a class of stochastic experts, where each expert is a conditional distribution over the arms given a context. We propose upper-confidence bound (UCB) algorithms for this problem, which employ two different importance sampling based estimators for the mean reward for each expert. Both these estimators leverage information leakage among the experts, thus using samples collected under all the experts to estimate the mean reward of any given expert. This leads to instance dependent regret bounds of $\mathcal{O}\left(λ(\pmb{μ})\mathcal{M}\log T/∆\right)$, where $λ(\pmb{μ})$ is a term that depends on the mean rewards of the experts, $∆$ is the smallest gap between the mean reward of the optimal expert and the rest, and $\mathcal{M}$ quantifies the information leakage among the experts. We show that under some assumptions $λ(\pmb{μ})$ is typically $\mathcal{O}(\log N)$. We implement our algorithm with stochastic experts generated from cost-sensitive classification oracles and show superior empirical performance on real-world datasets, when compared to other state of the art contextual bandit algorithms.

Motivated by settings such as hyper-parameter tuning and physical simulations, we consider the problem of black-box optimization of a function. Multi-fidelity techniques have become popular for applications where exact function evaluations are expensive, but coarse (biased) approximations are available at much lower cost. A canonical example is that of hyper-parameter selection in a learning algorithm. The learning algorithm can be trained for fewer iterations – this results in a lower cost, but its validation error is only coarsely indicative of the same if the algorithm had been trained till completion. We incorporate the multi-fidelity setup into the powerful framework of black-box optimization through hierarchical partitioning. We develop tree-search based multi-fidelity algorithms with theoretical guarantees on simple regret. We finally demonstrate the performance gains of our algorithms on both real and synthetic datasets.

Emerging 5G systems will need to efficiently support both broadband traffic (eMBB) and ultra-low-latency (URLLC) traffic. In these systems, time is divided into slots which are further sub-divided into minislots. From a scheduling perspective, eMBB resource allocations occur at slot boundaries, whereas to reduce latency URLLC traffic is pre-emptively overlapped at the minislot timescale, resulting in selective superposition/puncturing of eMBB allocations. This approach enables minimal URLLC latency at a potential rate loss to eMBB traffic. We study joint eMBB and URLLC schedulers for such systems, with the dual objectives of maximizing utility for eMBB traffic while satisfying instantaneous URLLC demands. For a linear rate loss model (loss to eMBB is linear in the amount of superposition/puncturing), we derive an optimal joint scheduler. Somewhat counter-intuitively, our results show that our dual objectives can be met by an iterative gradient scheduler for eMBB traffic that anticipates the expected loss from URLLC traffic, along with an URLLC demand scheduler that is oblivious to eMBB channel states, utility functions and allocations decisions of the eMBB scheduler. Next we consider a more general class of (convex) loss models and study optimal online joint eMBB/URLLC schedulers within the broad class of channel state dependent but time-homogeneous policies. We validate the characteristics and benefits of our schedulers via simulation.

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to switch OFF dynamically a subset of BSs to minimize energy costs. We consider two types of energy cost: 1) the cost of maintaining a BS in the active state and 2) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach-a Max-Weight algorithm along with a Lyapunov-based stability argument-does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight-based channel scheduler that has fast temporal dynamics. We show that using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are $L$ observed contexts and $K$ arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality $m$ ($m ≪L,K$). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the $L \times K$ mean reward matrix $\mathbfU$ (for each context in $[L]$ and each arm in $[K]$) factorizes into non-negative factors $\mathbfA$ ($L \times m$) and $\mathbfW$ ($m \times K$). This insight enables us to propose an $ε$-greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of $\mathcalO\left(L\mathrmpoly(m, \log K) \log T \right)$ at time $T$, as compared to $\mathcalO(LK\log T)$ for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of $\mathcalO\left(Km\log T\right)$. These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets.

Motivated by applications in computational advertising and systems biology, we consider the problem of identifying the best out of several possible soft interventions at a source node $V$ in an acyclic causal directed graph, to maximize the expected value of a target node $Y$ (located downstream of $V$). Our setting imposes a fixed total budget for sampling under various interventions, along with cost constraints on different types of interventions. We pose this as a best arm identification bandit problem with $K$ arms, where each arm is a soft intervention at $V$ and leverage the information leakage among the arms to provide the first gap dependent error and simple regret bounds for this problem. Our results are a significant improvement over the traditional best arm identification results. We empirically show that our algorithms outperform the state of the art in the Flow Cytometry data-set, and also apply our algorithm for model interpretation of the Inception-v3 deep net that classifies images.

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to opportunistically switch off a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach - a Max-Weight algorithm along with a Lyapunov-based stability argument - does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine whether $X \independent Y \vert Z$. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution $f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X \independent Y \vert Z.$ -- when given access only to i.i.d. samples from the true joint distribution $f(x,y,z)$. To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to $f^{CI}$ in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d \textit{near-independent} samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.

With increasing data demand, wireless networks are evolving to a hierarchical architecture where coverage is provided by both wide-area base stations (BS) and dense deployments of short-range access nodes (ANs) (e.g., small cells). The dense scale and mobility of users provide new challenges for scheduling: 1) high flux in mobile-to-AN associations, where mobile nodes quickly change associations with ANs (time scale of seconds) due to their small footprint and 2) multi-point connectivity, where mobile nodes are simultaneously connected to several ANs at any time. We study such a densified scenario with multi-channel wireless links (e.g., multi-channel OFDM) between nodes (BS/AN/mobile). We first show that traditional algorithms that forward each packet at most once, either to a single AN or a mobile user, do not have good delay performance. We argue that the fast association dynamics between ANs and mobile users necessitate a multi-point relaying strategy, where multiple ANs have duplicate copies of the data, and coordinate to deliver data to the mobile user. Surprisingly, despite data replication and no coordination between ANs, we show that our algorithm (a distributed scheduler-DIST) can approximately stabilize the system in large-scale instantiations of this setting, and further, performs well from a queue-length/delay perspective (shown via large deviation bounds).

We consider a variant of the multiarmed bandit problem where jobs queue for service, and service rates of different servers may be unknown. We study algorithms that minimize queue-regret: the (expected) difference between the queue-lengths obtained by the algorithm, and those obtained by a genie-aided matching algorithm that knows exact service rates. A naive view of this problem would suggest that queue-regret should grow logarithmically: since queue-regret cannot be larger than classical regret, results for the standard MAB problem give algorithms that ensure queue-regret increases no more than logarithmically in time. Our paper shows surprisingly more complex behavior. In particular, the naive intuition is correct as long as the bandit algorithm's queues have relatively long regenerative cycles: in this case queue-regret is similar to cumulative regret, and scales (essentially) logarithmically. However, we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is O(1/t). We demonstrate an algorithm that (order-wise) achieves this asymptotic queue-regret, and also exhibits close to optimal switching time from the early stage to the late stage.

In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the search problem of this paper aims to only find the nodes in a single such community, the target, out of the many communities that may exist. To do so , we are given suitable side information about the target; for example, a very small number of nodes from the target are labeled as such. We consider a general yet simple notion of side information: all nodes are assumed to have random weights, with nodes in the target having higher weights on average. Given these weights and the graph, we develop a variant of the method of moments that identifies nodes in the target more reliably, and with lower computation, than generic community detection methods that do not use side information and partition the entire graph.

In several data center settings, each arriving job may only be served by one of a subset of servers. Such a graph constraint can arise due to several reasons. One is locality of the data needed by a job; for example, in content farms (e.g., in Netflix or YouTube) a video request can only be served by a machine that possesses a copy. Motivated by this, we consider a setting where each job, on arrival, reveals a deadline and a subset of servers that can serve it. The job needs to be immediately allocated to one of these servers, and cannot be moved thereafter. Our objective is to maximize the fraction of jobs that are served before their deadlines. For this online load balancing problem, we prove an upper bound of 1-1/e on the competitive ratio of nonpreemptive online algorithms for systems with a large number of servers. We propose an algorithm - INSERT RANKING - which achieves this upper bound. The algorithm makes decisions in a correlated random way and it is inspired by the work of Karp, Vazirani, and Vazirani on online matching for bipartite graphs. We also show that two more natural algorithms, based on independent randomness, are strictly suboptimal, with a competitive ratio of 1/2.

In many networks the operator is faced with nodes that report a potentially important phenomenon such as failures, illnesses, and viruses. The operator is faced with the question: Is it spreading over the network, or simply occurring at random? We seek to answer this question from highly noisy and incomplete data, where at a single point in time we are given a possibly very noisy subset of the infected population (including false positives and negatives). While previous work has focused on uniform spreading rates for the infection, heterogeneous graphs with unequal edge weights are more faithful models of reality. Critically, the network structure may not be fully known and modeling epidemic spread on unknown graphs relies on non-homogeneous edge (spreading) weights. Such heterogeneous graphs pose considerable challenges, requiring both algorithmic and analytical development. We develop an algorithm that can distinguish between a spreading phenomenon and a randomly occurring phenomenon while using only local information and not knowing the complete network topology and the weights. Further, we show that this algorithm can succeed even in the presence of noise, false positives and unknown graph edges.

Motivated by emerging big streaming data processing paradigms (e.g., Twitter Storm, Streaming MapReduce), we investigate the problem of scheduling graphs over a large cluster of servers. Each graph is a job, where nodes represent compute tasks and edges indicate data-flows between these compute tasks. Jobs (graphs) arrive randomly over time, and upon completion, leave the system. When a job arrives, the scheduler needs to partition the graph and distribute it over the servers to satisfy load balancing and cost considerations. Specifically, neighboring compute tasks in the graph that are mapped to different servers incur load on the network; thus a mapping of the jobs among the servers incurs a cost that is proportional to the number of "broken edges''. We propose a low complexity randomized scheduling algorithm that, without service preemptions, stabilizes the system with graph arrivals/departures; more importantly, it allows a smooth trade-off between minimizing average partitioning cost and average queue lengths. Interestingly, to avoid service preemptions, our approach does not rely on a Gibbs sampler; instead, we show that the corresponding limiting invariant measure has an interpretation stemming from a loss system.

Personalized recommender systems provide great opportunities for targeted advertisements, by displaying ads alongside genuine recommendations. We consider a biased recommendation system where such ads are displayed without any tags (disguised as genuine recommendations), rendering them indistinguishable to users. We consider the problem of detecting such a bias and propose an algorithm that uses statistical analysis based on binary feedback data from a subset of users. We prove that the proposed algorithm detects bias with high probability for a broad class of recommendation systems with sufficient number of feedback samples.

We consider the problem of detecting an epidemic in a population where individual diagnoses are extremely noisy. We show that exclusively local, approximate knowledge of the contact network suffices to accurately detect the epidemic. The motivation for this problem is the plethora of examples (influenza strains in humans, or computer viruses in smartphones, etc.) where reliable diagnoses are scarce, but noisy data plentiful. In flu or phone-viruses, exceedingly few infected people/phones are professionally diagnosed (only a small fraction go to a doctor) but less reliable secondary signatures (e.g., people staying home, or greater-than-typical upload activity) are more readily available.

We study device-to-device (D2D) enabled hierarchical cellular networks consisting of a macro base station (BS), a dense network of access nodes (ANs) and mobile users, where spectrum is shared between cellular traffic and D2D traffic. Further, (the receivers of) mobile users dynamically time-share between the cellular and D2D networks. We develop algorithms for channel allocation and mobile-user receiver mode selection (choosing which network to participate in) with the objectives of minimizing delay for cellular traffic, and capacity maximization for D2D traffic. Our proposed solution takes advantage of the unique features offered by large and densified cellular networks such as multi-point connectivity, channel diversity, spatial reuse and load distribution. Given a BS-to-mobile delay requirement of d + 1 time-slots, we show that by appropriately scheduling channels and receiver modes, we can (with exponentially high probability) guarantee that cellular traffic reaches its intended destination within d timeslots. By leveraging spatial channel reuse, we show that this is achieved by utilizing a vanishingly small fraction of the available spatial capacity. Further, in the presence of delay-constrained cellular traffic, our scheduling algorithm guarantees D2D traffic can achieve rates within a (1-1/d) factor of the corresponding achievable rates without cellular traffic.

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV, and most computer viruses spread person to person, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper, we study two fundamental questions of detection. First, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread-the causative network-without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions that networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the d-dimensional grid, and the Erdös-Renyi graphs.

We propose new greedy algorithms for learning the structure of a graphical model of a probability distribution, given samples drawn from the distribution. While structure learning of graphical models is a widely studied problem with several existing methods, greedy approaches remain attractive due to their low computational cost. The most natural greedy algorithm would be one which, essentially, adds neighbors to a node in sequence until stopping; it would do this for each node. While it is fast, simple and parallel, this naive greedy algorithm has the tendency to add non-neighbors that show high correlations with the given node. Our new algorithms overcome this problem in three different ways. The recursive greedy algorithm iteratively recovers the neighbors by running the greedy algorithm in an inner loop, but each time only adding the last added node to the neighborhood set. The second forward-backward greedy algorithm includes a node deletion step in each iteration that allows non-neighbors to be removed from the neighborhood set which may have been added in the previous steps. Finally, the greedy algorithm with pruning runs the greedy algorithm until completion and then removes all the incorrect neighbors. We provide both analytical guarantees and empirical performance for our algorithms. We show that in graphical models with strong non-neighbor interactions, our greedy algorithms can correctly recover the graph, whereas the previous greedy and convex optimization-based algorithms do not succeed.

We study routing and scheduling algorithms for relay-assisted, multichannel downlink wireless networks [e.g., orthogonal frequency-division multiplexing (OFDM)-based cellular systems with relays]. Over such networks, while it is well understood that the BackPressure algorithm is stabilizing (i.e., queue lengths do not become arbitrarily large), its performance (e.g., delay, buffer usage) can be poor. In this paper, we study an alternative-the MaxWeight algorithm-variants of which are known to have good performance in a single-hop setting. In a general relay setting, however, MaxWeight is not even stabilizing (and thus can have very poor performance). In this paper, we study an iterative MaxWeight algorithm for routing and scheduling in downlink multichannel relay networks. We show that, surprisingly, the iterative MaxWeight algorithm can stabilize the system in several large-scale instantiations of this setting (e.g., general arrivals with full-duplex relays, bounded arrivals with half-duplex relays). Furthermore, using both many-channel large-deviations analysis and simulations, we show that iterative MaxWeight outperforms the BackPressure algorithm from a queue-length/delay perspective.

We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources unconstrained by the graph, but possessing a limited infection rate or virulence. Such a model captures many existing models of externally aided epidemics, and finds use in many settings - epidemiology, marketing and advertising, network robustness, etc. We provide a detailed characterization of the impact of external agents on epidemic thresholds. In particular, for the SIS model, we show that any external infection strategy with constant virulence either fails to significantly affect the lifetime of an epidemic, or at best, sustains the epidemic for a lifetime which is polynomial in the number of nodes. On the other hand, a random external-infection strategy, with rate increasing linearly in the number of infected nodes, succeeds under some conditions to sustain an exponential epidemic lifetime. We obtain similar sharp thresholds for the SIR model, and discuss the relevance of our results in a variety of settings.

We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint is motivated by modern social networks, wherein messages are broadcast to all neighbors, but attention spans are limited. Bounded susceptibility also arises in distributed computing applications with download bandwidth constraints, and in human epidemics under quarantine policies.

In this paper we look at content placement in the high-dimensional regime: there are n servers, and O(n) distinct types of content. Each server can store and serve O(1) types at any given time. Demands for these content types arrive, and have to be served in an online fashion; over time, there are a total of O(n) of these demands. We consider the algorithmic task of content placement: determining which types of content should be on which server at any given time, in the setting where the demand statistics (i.e. the relative popularity of each type of content) are not known a-priori, but have to be inferred from the very demands we are trying to satisfy. This is the high-dimensional regime because this scaling (everything being O(n)) prevents consistent estimation of demand statistics; it models many modern settings where large numbers of users, servers and videos/webpages interact in this way.

Topic modeling refers to the task of inferring, only from data, the abstract ``topics" that occur in a collection of content. In this paper we look at latent topic modeling in a setting where unlike traditional topic modeling (a) there are no/few features (like words in documents) that are directly indicative of content topics (e.g. un-annotated videos and images, URLs etc.), but (b) users share and view content over a social network. We provide a new algorithm for inferring both the topics in which every user is interested, and thus also the topics in each content piece. We study its theoretical performance and demonstrate its empirical effectiveness over standard topic modeling algorithms.

We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-à-vis the underlying network topology. For networks, which are spatially constrained, we show that the spread of infection can be significantly speeded up even by a few such external agents infecting randomly. Moreover, for general networks, we derive upper bounds on the order of the spreading time achieved by certain simple (random/greedy) external-spreading policies. Conversely, for certain common classes of networks such as line graphs, grids, and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external-spreading policies; these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with a random spreading policy. This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for spreading in such spatially constrained networks.

The problem of designing scheduling algorithms for a multichannel (e.g., orthogonal frequency division multiplexing-based) wireless downlink network is considered. The classic MaxWeight algorithm, although throughput-optimal, results in a very poor per-user delay performance in such systems. Hence, an alternate class of algorithms called iterated longest queues first (iLQF) is proposed for overcoming this issue. The iLQF-class algorithms are analyzed in a number of different system configurations. A particular algorithm in this class, called iLQF with pullup, is shown to be rate function optimal for the problem in an appropriate large deviations setting, and is shown to result in a strictly positive value of the rate function for a number of modifications to the basic system model. Thus, the proposed algorithm yields provable performance guarantees. The analytic results are confirmed through simulations.

We study routing and scheduling algorithms for relay-assisted, multi-channel downlink wireless networks (e.g., OFDM-based cellular systems with relays). Over such networks, while it is well understood that the BackPressure algorithm is stabilizing (i.e., queue lengths do not become arbitrarily large), its performance (e.g., delay, buffer usage) can be poor. In this paper, we study an alternative - the MaxWeight algorithm - variants of which are known to have good performance in a single-hop setting. In a general relay setting however, MaxWeight is not even stabilizing (and thus can have very poor performance). In this paper, we study an iterative MaxWeight algorithm for routing and scheduling in downlink multi-channel relay networks. We show that, surprisingly, the iterative MaxWeight algorithm can stabilize the system in several large-scale instantiations of this setting (e.g., general arrivals with full-duplex relays, bounded arrivals with half-duplex relays). Further, using both many-channel large-deviations analysis and simulations, we show that iterative MaxWeight outperforms the BackPressure algorithm from a queue-length/delay perspective.

From Cholera, AIDS/HIV, and Malaria, to rumors and viral video, understanding the causative network behind an epidemic's spread has repeatedly proven critical for managing the spread (controlling or encouraging, as the case may be). Our current approaches to understand and predict epidemics rely on the scarce, but exact/reliable, expert diagnoses. This paper proposes a different way forward: use more readily available but also more noisy data with {\em many false negatives and false positives}, to determine the causative network of an epidemic. Specifically, we consider an epidemic that spreads according to one of two networks. At some point in time we see a small random subsample (perhaps a vanishingly small fraction) of those infected, along with an order-wise similar number of false positives. We derive sufficient conditions for this problem to be detectable, and provide an efficient algorithm that solves the hypothesis testing problem. We apply this model to two settings. In the first setting, we simply want to distinguish between random illness (a complete graph) and an epidemic (spread along a structured graph). In the second, we have a superposition of both of these, and we wish to detect which is the strongest component.

In several data center settings, each arriving job may only be served by one of a subset of servers. Such a graph constraint can arise due to several reasons. One is locality of the data needed by a job; for example, in content farms (e.g. in Netflix or YouTube) a video request can only be served by a machine that possesses a copy. Motivated by this, we consider a setting where each job, on arrival, reveals a deadline and a subset of servers that can serve it. The job needs to be immediately allocated to one of these servers, and cannot be moved thereafter. Our objective is to maximize the fraction of jobs that are served before their deadlines. For this online load balancing problem, we prove an upper bound of 1-1/e on the competitive ratio of non-preemptive online algorithms for systems with a large number of servers. We propose an algorithm - INSERT RANKING - which achieves this upper bound. The algorithm makes decisions in a correlated random way and it is inspired by the work of Karp, Vazirani and Vazirani on online matching for bipartite graphs. We also show that two more natural algorithm, based on independent randomness, are strictly suboptimal, with a competitive ratio of 1/2.

We consider information dissemination in a largen-user wireless network in whichkusers wish to share a unique message with all other users. Each of thenusers only has knowledge of its own contents and state information; this corresponds to a one-sided push-only scenario. The goal is to disseminate all messages efficiently, hopefully achieving an order-optimal spreading rate over unicast wireless random networks. First, we show that a random-push strategy-where a user sends its own or a received packet at random-is order-wise suboptimal in a random geometric graph: specifically, Ω(√n) times slower than optimal spreading. It is known that this gap can be closed if each user has “full” mobility, since this effectively creates a complete graph. We instead consider velocity-constrained mobility where at each time slot the user moves locally using a discrete random walk with velocityv(n) that is much lower than full mobility. We propose a simple two-stage dissemination strategy that alternates between individual message flooding (“self promotion”) and random gossiping. We prove that this scheme achieves a close to optimal spreading rate (within only a logarithmic gap) as long as the velocity is at leastv(n)=ω(√(logn/k)). The key insight is that the mixing property introduced by the partial mobility helps users to spread in space within a relatively short period compared to the optimal spreading time, which macroscopically mimics message dissemination over a complete graph.

This paper proposes FlashLinQ-a synchronous peer-to-peer wireless PHY/MAC network architecture. FlashLinQ leverages the fine-grained parallel channel access offered by OFDM and incorporates an analog energy-level-based signaling scheme that enables signal-to-interference ratio (SIR)-based distributed scheduling. This new signaling mechanism, and the concomitant scheduling algorithm, enables efficient channel-aware spatial resource allocation, leading to significant gains over a CSMA/CA system using RTS/CTS. FlashLinQ is a complete system architecture including: 1) timing and frequency synchronization derived from cellular spectrum; 2) peer discovery; 3) link management; and 4) channel-aware distributed power, data rate, and link scheduling. FlashLinQ has been implemented for operation over licensed spectrum on a digital signal processor/field-programmable gate array (DSP/FPGA) platform. In this paper, we present FlashLinQ performance results derived from both measurements and simulations.

We consider a server serving a time-slotted queued system of multiple packet-based flows, where not more than one flow can be serviced in a single time slot. The flows have exogenous packet arrivals and time-varying service rates. At each time, the server can observe instantaneous service rates for only a subset of flows (selected from a fixed collection of observable subsets) before scheduling a flow in the subset for service. We are interested in queue-length aware scheduling to keep the queues short. The limited availability of instantaneous service rate information requires the scheduler to make a careful choice of which subset of service rates to sample. We develop scheduling algorithms that use only partial service rate information from subsets of channels, and that minimize the likelihood of queue overflow in the system. Specifically, we present a new joint subset-sampling and scheduling algorithm called Max-Exp that uses only the current queue lengths to pick a subset of flows, and subsequently schedules a flow using the Exponential rule. When the collection of observable subsets is disjoint, we show that Max-Exp achieves the best exponential decay rate, among all scheduling algorithms using partial information, of the tail of the longest queue in the system. To accomplish this, we introduce novel analytical techniques for studying the performance of scheduling algorithms using partial state information, that are of independent interest. These include new sample-path large deviations results for processes obtained by nonrandom, predictable sampling of sequences of independent and identically distributed random variables, which show that scheduling with partial state information yields a rate function significantly different from the case of full information. As a special case, Max-Exp reduces to simply serving the flow with the longest queue when the observable subsets are singleton flows, i.e., when there is effectively no a priori channel-state information; thus, our results show that this greedy scheduling policy is large-deviations optimal.

Greedy Maximal Scheduling (GMS) is an attractive low-complexity scheme for scheduling in wireless networks. Recent work has characterized its throughput for the case when there is no fading/channel variations. This paper aims to understand the effect of channel variations on the relative throughput performance of GMS vis-a-vis that of an optimal scheduler facing the same fading. The effect is not a-priori obvious because, on the one hand, fading could help by decoupling/precluding global states that lead to poor GMS performance, while on the other hand fading adds another degree of freedom in which an event unfavorable to GMS could occur. We show that both these situations can occur when fading is adversarial. In particular, we first define the notion of a Fading Local Pooling factor (F-LPF), and show that it exactly characterizes the throughput of GMS in this setting. We also derive general upper and lower bounds on F-LPF. Using these bounds, we provide two example networks - one where the relative performance of GMS is worse than if there were no fading, and one where it is better.

Computer (and human) networks have long had to contend with spreading viruses. Effectively controlling or curbing an outbreak requires understanding the dynamics of the spread. A virus that spreads by taking advantage of physical links or user-acquaintance links on a social network can grow explosively if it spreads beyond a critical radius. On the other hand, random infections (that do not take advantage of network structure) have very different propagation characteristics. If too many machines (or humans) are infected, network structure becomes essentially irrelevant, and the different spreading modes appear identical. When can we distinguish between mechanics of infection? Further, how can this be done efficiently? This paper studies these two questions. We provide sufficient conditions for different graph topologies, for when it is possible to distinguish between a random model of infection and a spreading epidemic model, with probability of misclassification going to zero. We further provide efficient algorithms that are guaranteed to work in different regimes.

A time-slotted queueing system for a wireless downlink with multiple flows and a single server is considered, with exogenous arrivals and time-varying channels. It is assumed that only one user can be serviced in a single time slot. Unlike much recent work on this problem, attention is drawn to the case where the server can obtain only partial information about the instantaneous state of the channel. In each time slot, the server is allowed to specify a single subset of flows from a collection of observable subsets, observe the current service rates for that subset, and subsequently pick a user to serve. The stability region for such a system is provided. An online scheduling algorithm is presented that uses information about marginal distributions to pick the subset and the Max-Weight rule to pick a flow within the subset, and which is provably throughput-optimal. In the case where the observable subsets are all disjoint, or where the subsets and channel statistics are symmetric, it is shown that a simple scheduling algorithm-Max-Sum-Queue-that essentially picks subsets having the largest squared-sum of queues, followed by picking a user using Max-Weight within the subset, is throughput-optimal.

This paper considers the problem of designing scheduling algorithms for multichannel (e.g., OFDM-based) wireless downlink networks, with a large number of users and proportionally large bandwidth. For this system, while the classical MaxWeight algorithm is known to be throughput-optimal, its buffer-overflow performance is very poor (formally, it is shown that it has zero rate function in our setting). To address this, a class of algorithms called iterated Heaviest matching with Longest Queues First (iHLQF) is proposed. The algorithms in this class are shown to be throughput-optimal for a general class of arrival/channel processes, and also rate-function-optimal (i.e., exponentially small buffer overflow probability) for certain arrival/channel processes. iHLQF, however, has higher complexity than MaxWeight (n4versusn2, respectively). To overcome this issue, a new algorithm called Server-Side Greedy (SSG) is proposed. It is shown that SSG is throughput-optimal, results in a much better per-user buffer overflow performance than the MaxWeight algorithm (positive rate function for certain arrival/channel processes), and has a computational complexity (n2) that is comparable to the MaxWeight algorithm. Thus, it provides a nice tradeoff between buffer-overflow performance and computational complexity. These results are validated by both analysis and simulations.

We study an intermittently connected network (ICN) composed of multiple clusters of wireless nodes. Within each cluster, nodes can communicate directly using the wireless links. However, these clusters are far away from each other such that direct communication between the clusters is impossible except through “mobile” contact nodes. These mobile contact nodes are data carriers that shuffle between clusters and transport data from the source to the destination clusters. There are several applications of our network model, such as clusters of mobile soldiers connected via unmanned aerial vehicles. Our work here focuses on a queue-based cross-layer technique known as the back-pressure algorithm. The algorithm is known to be throughput-optimal, as well as resilient to disruptions in the network, making it an ideal candidate communication protocol for our intermittently connected network. In this paper, we design a back-pressure routing/rate control algorithm for ICNs. Though it is throughput-optimal, the back-pressure algorithm has several drawbacks when used in ICNs, including long end-to-end delays, large number of potential queues needed, and loss in throughput due to intermittency. We present a modified back-pressure algorithm that addresses these issues. We implement our algorithm on a 16-node experimental testbed and present our experimental results in this paper.

This paper considers the problem of designing scheduling algorithms for multi-channel (e.g., OFDM-based) wireless downlink systems. We show that the Server-Side Greedy (SSG) rule introduced in earlier papers for ON-OFF channels performs well even for more general channel models. The key contribution in this paper is the development of new mathematical techniques for analyzing Markov chains that arise when studying general channel models. These techniques include a way of calculating the distribution of the maximum of a multi-dimensional Markov chain (note that the maximum does not have the Markov property on its own), and also a Markov chain stochastic dominance result using coupling arguments.

Information dissemination in a large network is typically achieved when each user shares its own information or resources with each other user. Consider n users randomly located over a fixed region, and k of them wish to flood their individual messages among all other users, where each user only has knowledge of its own contents and state information. The goal is to disseminate all messages using a low-overhead strategy that is one-sided and distributed while achieving an order-optimal spreading rate over a random geometric graph. In this paper, we investigate the random-push gossip-based algorithm where message selection is based on the sender's own state in a random fashion. It is first shown that random-push is inefficient in static random geometric graphs. Specifically, it is Ω(√n) times slower than optimal spreading. This gap can be closed if each user is mobile, and at each time moves “locally” using a random walk with velocity v(n). We propose an efficient dissemination strategy that alternates between individual message flooding and random gossiping. We show that this scheme achieves the optimal spreading rate as long as the velocity satisfies v(n) = ω(√log n/k). The key insight is that the mixing introduced by this velocity-limited mobility approximately uniformizes the locations of all copies of each message within the optimal spreading time, which emulates a balanced geometry-free evolution over a complete graph.

We study infection spreading on large static networks when the spread is assisted by a small number of additional virtually mobile agents. For networks which are “spatially constrained”, we show that the spread of infection can be significantly sped up even by a few virtually mobile agents acting randomly. More specifically, for general networks with bounded virulence (e.g., a single or finite number of random virtually mobile agents), we derive upper bounds on the order of the time taken (as a function of network size) for infection to spread. Conversely, for certain common classes of networks such as linear graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) virtual mobility strategies. We show that up to a logarithmic factor, these lower bounds for adversarial virtual mobility match the upper bounds on spreading via an agent with random virtual mobility. This demonstrates that random, state-oblivious virtual mobility is in fact order-wise optimal for dissemination in such spatially constrained networks.

We seek to develop joint aggregation, routing, and scheduling algorithms that, for any graph topology and a large class of functions, have analytically provable performance benefits due to in-network computation as compared to simple data forwarding. To this end, we define a class of functions, the Fully-Multiplexible functions, which includes several functions such as parity, k-th order statistic and range, and for which we can exactly characterize the maximum achievable refresh rate of the network in terms of an underlying graph primitive, the min-mincut. In wireline networks, we show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless networks, we provide a MaxWeight-like algorithm with dynamic flow splitting that is shown to be throughput-optimal.

We consider the problem of broadcasting a large file over a wireless network (e.g., students in a campus). If each user who wants the file must download it from the carrier's WAN, dissemination time scales linearly. Two often-occurring facts suggest we can do better: (a) the demand for the file often spreads via a social network (e.g., Facebook); and (b) the devices predominantly used are GPS enabled, and equipped with a peer-to-peer (ad hoc) transmission mode. The premise of this paper is that (a) and (b) are often the case. Starting from here, we consider this coupled-network problem (demand on the social network; bandwidth on the wireless network) and taking advantage of the fact that the two networks have different topologies, we propose a file dissemination algorithm. In our scheme, users query their social network to find geographically nearby friends that have the desired file, and utilize the underlying ad hoc network to route the data via multi-hop transmissions. We show that for many popular models for social networks, the file dissemination time scales sublinearly with the number of users.

Recent deployments of data-rich smart phones has provided a fresh impetus for designing, deploying and understanding the performance of wide area ad-hoc networks. The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In this paper, using tools from stochastic geometry, we study and optimize the throughput performance of such networks. We show that in ad-hoc networks enabled with SIR based scheduling, a simple modification to the transmit power level - setting it to be inversely proportional to the square root of the link gain - leads to large improvements in network throughput. This simple power-level selection is optimal over the class of all ”local” transmit power selection strategies when channels are stationary, and further is at most a factor of two away from optimality in the fading case. Using stochastic geometric techniques, we also provide analytical expressions for the medium access probability in different scenarios.

In this paper, we consider a network of stationary nodes that rely on mobile nodes to transport data between them. We assume the mobile nodes can control their mobility pattern to respond to traffic loads, as well as satisfy some other secondary objectives, such as surveillance requirements. We study this problem in the framework of cost minimization, where we derive a dual iterative algorithm that results in optimal mobility pattern for minimizing network wide cost. We then implement our proposed algorithm and evaluate its performance on a testbed.

The problem of routing/scheduling in a wireless network with partial/delayed network (channel and queue) state information (NSI) is studied in this paper. Two cases are considered: (i) centralized routing/scheduling, where a central controller obtains heterogeneously delayed information from each of the nodes (thus, the controller has NSI with different delays from different nodes), and makes routing/scheduling decisions; (ii) decentralized routing/scheduling, where each node makes a decision based on its current channel and queue states along with homogeneous delayed NSI from other nodes. For each of the cases (with additional flow restrictions for the decentralized routing/scheduling case), the optimal network throughput regions are characterized under the above described NSI models and it is shown that the throughput regions shrinks with the increase of delay. Further, channel and queue length based routing/scheduling algorithms that achieve the above throughput regions are proposed in this paper.

Back-pressure-type algorithms based on the algorithm by Tassiulas and Ephremides have recently received much attention for jointly routing and scheduling over multihop wireless networks. However, this approach has a significant weakness in routing because the traditional back-pressure algorithm explores and exploits all feasible paths between each source and destination. While this extensive exploration is essential in order to maintain stability when the network is heavily loaded, under light or moderate loads, packets may be sent over unnecessarily long routes, and the algorithm could be very inefficient in terms of end-to-end delay and routing convergence times. This paper proposes a new routing/scheduling back-pressure algorithm that not only guarantees network stability (throughput optimality), but also adaptively selects a set of optimal routes based on shortest-path information in order to minimize average path lengths between each source and destination pair. Our results indicate that under the traditional back-pressure algorithm, the end-to-end packet delay first decreases and then increases as a function of the network load (arrival rate). This surprising low-load behavior is explained due to the fact that the traditional back-pressure algorithm exploits all paths (including very long ones) even when the traffic load is light. On the other-hand, the proposed algorithm adaptively selects a set of routes according to the traffic load so that long paths are used only when necessary, thus resulting in much smaller end-to-end packet delays as compared to the traditional back-pressure algorithm .

This paper considers the problem of designing scheduling algorithms for multi-channel (e.g., OFDM) wireless downlink networks with n users/OFDM sub-channels. For this system, while the classical MaxWeight algorithm is known to be throughput-optimal, its buffer-overflow performance is very poor (formally, we show it has zero rate function in our setting). To address this, we propose a class of algorithms called iHLQF (iterated Heaviest matching with Longest Queues First) that is shown to be throughput optimal for a general class of arrival/channel processes, and also rate-function optimal (i.e., exponentially small buffer overflow probability) for certain arrival/channel processes. iHLQF however has higher complexity than MaxWeight (n4vs. n2respectively). To overcome this issue, we propose a new algorithm called SSG (Server-Side Greedy). We show that SSG is throughput optimal, results in a much better per-user buffer overflow performance than the MaxWeight algorithm (positive rate function for certain arrival/channel processes), and has a computational complexity (n2) that is comparable to the MaxWeight algorithm. Thus, it provides a nice trade-off between buffer-overflow performance and computational complexity. These results are validated by both analysis and simulations.

We study a mobile wireless network where groups or clusters of nodes are intermittently connected via mobile "carriers'' (the carriers provide connectivity over time among different clusters of nodes). Over such networks (an instantiation of a delay tolerant network), it is well-known that traditional routing algorithms perform very poorly. In this paper, we propose a two-level Back- Pressure with Source-Routing algorithm (BP+SR) for such networks. The proposed BP+SR algorithm separates routing and scheduling within clusters (fast time-scale) from the communications that occur across clusters (slow time-scale), without loss in network throughput (i.e., BP+SR is throughput-optimal). More importantly, for a source and destination node that lie in different clusters, the traditional back-pressure algorithm results in large queue lengths at each node along its path. This is because the queue dynamics are driven by the slowest time-scale (i.e., that of the carrier nodes) along the path between the source and destination, which results in very large end-to-end delays. On the other-hand, we show that the two-level BP+SR algorithm maintains large queues only at a very few nodes, and thus results in order-wise smaller end-to-end delays. We provide analytical as well as simulation results to confirm our claims.

While there has been much progress in designing backpressure based stabilizing algorithms for multihop wireless networks, end-to-end performance (e.g., end-to-end buffer usage) results have not been as forthcoming. In this paper, we study the end-to-end buffer usage (sum of buffer utilization along a flow path) over a network with general topology and with fixed, loop-free routes using a large-deviations approach. We first derive bounds on the best performance that any scheduling algorithm can achieve. Based on the intuition from the bounds, we propose a class of (backpressure-like) scheduling algorithms called ¿ß-algorithms. We show that the parameters ¿ and ß can be chosen such that the system under the ¿ß-algorithm performs arbitrarily closely to the best possible scheduler (formally the decay rate function for end-to-end buffer overflow is shown to be arbitrarily close to optimal in the large-buffer regime). We also develop variants which have the same asymptotic optimality property, and also provide good performance in the small-buffer regime. Our results are substantiated using both analysis and simulation.

We study a network composed of multiple clusters of wireless nodes. Within each cluster, nodes can communicate directly using the wireless links; however, these clusters are far away such that direct communication between the clusters is impossible except through "mobile" contact nodes. These mobile contact nodes are data carriers that shuffle between clusters and transport data from source to destination clusters. There are several applications of our network model (e.g., clusters of mobile soldiers connected via unmanned aerial vehicles).

Traditionally, network buffer resources have been used at routers to queue transient packets to prevent packet drops. In contrast, we propose a scheme for large multihop networks where intermediate routers have no buffers for queueing transient packets. In the proposed scheme, network storage resources (memory) are used only at source and destination nodes to encode/decode packets using random linear coding over time. Our scheme capitalizes on the common empirical observation that for large networks with many flows through each router, if packet loss occurs in a flow path, it will very likely occur only at only a very few links on the path. Unfortunately, the location of this congested link varies with time, thereby preventing prevailing static buffer allocation strategies from exploiting this observation. We propose source coding over packets at the session layer as a means of “sharing” memory across links along a flow path. We call this spatial buffer multiplexing-where buffering and coding implemented at the source compensates for packet loss at any downstream bufferless link. First, we consider large spatial multihop networks withNnodes (each with finite buffer space for coding/decoding) and Θ(N) flows; the number of flows through each link scales as Ω(Nα) for some α ∈ (0,1). Using many-sources large deviations analysis, we show that to obtain comparable packet drop probabilities (QoS), spatial buffer multiplexing provides an order-wise buffer gain of Ω(Nα) per node over traditional static buffer allocation for queueing. Next we consider the complementary case of a network with a small number of flows through a buffer, but large source buffer. Here, we provide a sufficient condition under which the packet loss probability decreases exponentially in a function that is linear in the size of the input buffer, where the function is required to meet a predetermined negative slope -δ. We express the loss effective bandwidth for coding and compare it against that for queueing.

Geographic routing with greedy relaying strategies are important routing schemes in sensor networks. These schemes assume that the nodes have perfect information about the location of the destination. When the destination is unit distance away, the asymptotic routing delays are Θ(1/M(n)) , where M(n) is the maximum distance traveled in one hop (transmission range). We consider three scenarios where: i) nodes have location errors (imprecise GPS); ii) only coarse geographic information about the destination is available, e.g., the quadrant in which the destination is located; and iii) only a small fraction of the nodes have routing information. In this paper, we show that even with such limited destination-location information, the routing delays are Θ(1/ M(n)) , and validate our analysis with simulations. Finally, we consider the throughput-capacity of networks with progressive routing strategies that take packets closer to the destination in every step, but not necessarily along a straight-line. While such a routing strategy could lead to spatial “hotspots” due to the suboptimal flows nonuniformly loading the network, we show that the effect of hot spots due to progressive routing does not reduce the network throughput-capacity in an order sense, i.e., is order-wise the same as the maximum achievable throughput-capacity.

Aggregate traffic loads and topology in multihop wireless networks may vary slowly, permitting MAC protocols to “learn” how to spatially coordinate and adapt contention patterns. Such an approach could reduce contention, leading to better throughput. To that end, we propose a family of MAC scheduling algorithms and demonstrate general conditions, which, if satisfied, ensure lattice rate optimality (i.e., achieving any rate-point on a uniform discrete lattice within the throughput region). This general framework enables the design of MAC protocols that meet various objectives and conditions. In this paper, as instances of such a lattice-rate-optimal family, we propose distributed, synchronous contention-based scheduling algorithms that: 1) are lattice-rate-optimal under both the signal-to-interference-plus-noise ratio (SINR)-based and graph-based interference models; 2) do not require node location information; and 3) only require three-stage RTS/CTS message exchanges for contention signaling. Thus, the protocols are amenable to simple implementation and may be robust to network dynamics such as topology and load changes. Finally, we propose a heuristic, which also belongs to the proposed lattice-rate-optimal family of protocols and achieves faster convergence, leading to a better transient throughput.

Routing to mobile nodes in a wireless network is conventionally performed by associating a static IP address (or a geographic location) to each node, and routing to that address using routing tables at intermediate nodes that are updated periodically to reflect mobility-induced network topology changes. This mode of routing works when the mobiles' speeds as well as the number of mobiles are small. However, in the presence of large number of fast-moving mobiles, such approaches are infeasible and can lead to excessive overheads, routing failures and hence, throughput loss. In this paper, we consider a wireless network over a domain with a collection of static nodes (that form a connected cover of the domain) and mobile nodes, where the mobile nodes can move in an arbitrary (non-ergodic) manner over sub-domains of the network. For such a system, we develop new routing algorithms (based on a spatial multi-resolution search) that we show are efficient both in terms of routing overheads and throughput. In particular, we show that the achievable rate region of the proposed algorithm is within a poly-logarithmic constant of the optimal rate region with non-ergodic mobility.

We study throughput-optimal scheduling/routing over mobile ad-hoc networks with time-varying (fading) channels. Traditional back-pressure algorithms (based on the work by Tassiulas and Ephremides) require instantaneous network state (topology, queues-lengths, and fading channel-state) in order to make scheduling/routing decisions. However, such instantaneous network-wide (global) information is hard to come by in practice, especially when mobility induces a time-varying topology. With information delays and a lack of global network state, different mobile nodes have differing "views" of the network, thus inducing uncertainty and inconsistency across mobile nodes in their topology knowledge and network state information. In such a setting, we first characterize the through-optimal rate region and develop a back-pressure-like scheduling algorithm, which we show is throughput-optimal. Then, by partitioning the geographic region spatially into disjoint tiles, and sharing delayed topology and network state information only among mobile nodes currently within each tile, we develop a localized low-complexity scheduling algorithm. The algorithm uses instantaneous local information (the queue length, channel state and current position at a mobile node) along with delayed network state information from nodes that were within its tile (i.e., from nodes that were within a nearby geographic region as opposed to network-wide information). The proposed algorithm is shown to be near-optimal, where the geographic distance over which delayed network-state information is shared determines the provable lower bound on the achievable throughput.

Back-pressure based algorithms based on the algorithm by Tassiulas and Ephremides have recently received much attention for jointly routing and scheduling over multi-hop wireless networks. However a significant weakness of this approach has been in routing, because the traditional back-pressure algorithm explores and exploits all feasible paths between each source and destination. While this extensive exploration is essential in order to maintain stability when the network is heavily loaded, under light or moderate loads, packets may be sent over unnecessarily long routes and the algorithm could be very inefficient in terms of end-to-end delay and routing convergence times. This paper proposes new routing/scheduling back-pressure algorithms that not only guarantees network stability (through-put optimality), but also adaptively selects a set of optimal routes based on shortest-path information in order to minimize average path-lengths between each source and destination pair. Our results indicate that under the traditional back-pressure algorithm, the end-to-end packet delay first decreases and then increases as a function of the network load (arrival rate). This surprising low-load behavior is explained due to the fact that the traditional back-pressure algorithm exploits all paths (including very long ones) even when the traffic load is light. On the otherhand, the proposed algorithm adaptively selects a set of routes according to the traffic load so that long paths are used only when necessary, thus resulting in much smaller end-to-end packet delays as compared to the traditional back-pressure algorithm.

We consider the problem of throughput-optimal routing over large-scale wireless ad-hoc networks. Gupta and Kumar (2000) showed that a throughput capacity (a uniform rate over all source-destination pairs) of thetas( 1/radicn log n ) is achievable in random planar networks, and the capacity is achieved by straight-line routes. In reality, both the network model and the traffic demands are likely to be highly non-uniform. In this paper, we first propose a randomized forwarding strategy based on geographic routing that achieves near-optimal throughput over random planar networks with an arbitrary number of routing holes (regions devoid of nodes) of varying sizes. Next, we study a random planar network with arbitrary source-destination pairs with arbitrary traffic demands. For such networks, we demonstrate a randomized local load-balancing algorithm that supports any traffic load that is within a poly-logarithmic factor of the throughput region. Our algorithms are based on geographic routing and hence inherit their advantageous properties of low- complexity, robustness and stability.

This correspondence derives bounds on the jamming capacity of a slotted ALOHA system. A system with n legitimate users, each with a Bernoulli arrival process is considered. Packets are temporarily stored at the corresponding user queues, and a slotted ALOHA strategy is used for packet transmissions over the shared channel. The scenario considered is that of a pair ofillegitimateusers that jam legitimate transmissions in order to communicate over the slotted ALOHA channel. Jamming leads to binary signaling between the illegitimate users, with packet collisions due to legitimate users treated as (multiplicative) noise in this channel. Further, the queueing dynamics at the legitimate users stochastically couples the jamming strategy used by the illegitimate users and the channel evolution. By considering various independent and identically distributed (i.i.d.) jamming strategies, achievable jamming rates over the slotted ALOHA channel are derived. Further, an upper bound on the jamming capacity over the class of all ergodic jamming policies is derived. These bounds are shown to be tight in the limit where the offered system load approaches unity.

We consider the problem of aggregating data at a mobile fusion center (fusor) (eg. a PDA or a cellular phone) moving within a spatial region over which a wireless sensor network (eg., fixed motes) has been deployed. Each sensor node generates packets destined to the fusor, and our objective is to develop strategies that can route the packets to the mobile fusor. For an arbitrary (possibly random) fusor mobility pattern over any connected subset of the sensor deployment area, we first derive upper bounds on the aggregation data rate (i.e., the uniform rate region from each sensor node to the mobile fusor), where we allow all sensor nodes to have complete knowledge of the mobility pattern of the fusor. We then consider aggregation data rates that can be achieved when the mobility pattern of the fusor is unknown to the sensor nodes. Surprisingly, we show that for a class of mobility patterns (random mobility over connected-compositions of convex sets of the deployment region, e.g. random walks over piece-wise linear sets), we can construct "universal" mobility-oblivious routing strategies that achieve aggregation data rates that are of the same order as the (mobility-aware) upper bound.

Geographic forwarding has been widely studied as a routing strategy for large wireless networks, mainly due to the low complexity of the routing algorithm, scalability of the routing information with network size and fast convergence times of routes. On a planar network with no holes, Gupta and Kumar (2000) have shown that a uniform traffic demand of ominus(1/radicn log n) is achievable. However, in a network with routing holes (regions on the plane which do not have active nodes), geographic routing schemes such as GPSR or GOAFR could cause the throughput capacity to significantly drop due to concentration of traffic on the face of the holes. Similarly, geographic schemes could fail to support non-uniform traffic patterns due to spatial congestion (traffic concentration) caused by greedy "straight-line" routing. In this paper, we first propose a randomized geographic routing scheme that can achieve a throughput capacity of ominus(1/radicn) (within a poly-logarithmic factor) even in networks with routing holes. Thus, we show that our scheme is throughput optimal (up to a poly-logarithmic factor) while preserving the inherent advantages of geographic routing. We also show that the routing delay incurred by our scheme is within a poly-logarithmic factor of the optimal throughput-delay trade-off curve. Next, we construct a geographic forwarding based routing scheme that can support wide variations in the traffic requirements (as much as ominus(1) rates for some nodes, while supporting ominus(1/radicn) for others). We finally show that the above two schemes can be combined to support non-uniform traffic demands in networks with holes.

We propose a general family of MAC scheduling algorithms that achieve any rate-point on a uniform discrete-lattice within the throughput-region (i.e., lattice-throughput-optimal) under a physical interference model. Under the physical interference model, a centralized algorithm requires information on node locations (and distance among nodes) to determine a schedule that is provably throughput-optimal. In this paper, we propose a distributed, synchronous contention-based scheduling algorithm that (i) is lattice-throughput-optimal, (ii) does not require node location information, and (iii) has a signaling complexity that does not depend on network size. Thus, it is amenable to simple implementation, and is robust to network dynamics such as topology and load changes.

We develop order bounds on the refresh rate of computing functions over large multi-hop sensor networks, with finite degree (finite neighbors for each node). The refresh rate quantifies how often the function can be re-computed with new data at sensor nodes. Giridhar and Kumar (2005) considered deterministic function computation for two important classes of functions (type-threshold and type-sensitive functions) and showed that for networks with high degree (random planar geometric graph with n nodes and average degree Theta(log n)), type- threshold functions (e.g. max) are easy to compute (refresh rate of Theta(1/log(n))), and type-sensitive functions (e.g. average) can be computed only at a rate Theta(1/log(n)). In this paper, we first show that type-threshold functions can be computed at an optimal refresh rate of Theta(1) over networks with finite degree. However, the computation of type-sensitive function do not become uniformly faster as the graph degree becomes smaller. We demonstrate that while some type-sensitive functions (such as computing parity) are not hard to compute in finite degree graphs (we can achieve a refresh rate proportional to (1/d), where d is the maximum graph degree), there exist type-sensitive functions (e.g., computing the average to one-bit precision) in this class that cannot be deterministically computed faster than Theta(1/log n) even for finite degree graphs. However, by relaxing the requirements to allow probabilistic guarantees, computing the average can be achieved at a refresh rate of Theta(1) over any graph with bounded degree and a refresh rate of Theta(1/ log log n) for random planar networks. Further, for random planar networks operating over an AWGN channel with signal power path-loss, we show that even refresh rates of Theta(1) can be achieved with vanishing distortion when the power path- loss exponent is strictly less than 4. Thus, relaxing deterministic computation guarantees to probabilistic requirements enables sizea

Traditionally, network buffer resources have been used at routers to queue transient packets to prevent packet drops. In contrast, we propose a scheme for large multi-hop networks where intermediate routers have no buffers for queueing transient packets. In the proposed scheme, network storage resources (memory) are used only at source and destination nodes to encode/decode packets using random linear coding over time. Our scheme utilizes the observation that for large networks with many flows through each router, if packet loss occurs in a flow path, it will very likely occur only at only one link in the path. Unfortunately, the location of this congested link varies with time, hence, preventing static buffer allocation strategies from exploiting this observation. We propose network coding as a means of “sharing” memory across links along a flow path. We call this spatial buffer multiplexing – where buffering and coding implemented at the source compensates for packet loss at any downstream bufferless link. In this paper, we consider large spatial multi-hop networks with N nodes and Θ(N) flows, where the number of flows through each link scales as Ω(N) for some α ∈ (0, 1). Using many-sources large deviations analysis, we show that to obtain comparable packet drop probabilities (QoS), spatial buffer multiplexing provides an order-wise buffer gain of Ω(N) per node over traditional queueing.

Flooding based querying and broadcasting schemes have low hop-delays of Theta(1/R(n)) to reach any node that is a unit distance away, where R(n) is the transmission range of any sensor node. However, in sensor networks with large radio ranges, flooding based broadcasting schemes cause many redundant transmissions leading to a storm problem. In this paper, we study the role of geographic information and state information (i.e., memory of previous messages or transmissions) in reducing the redundant transmissions in the network. We consider three broadcasting schemes with varying levels of local information where nodes have: (i) no geographic or state information, (ii) coarse geographic information about the origin of the broadcast, and (Hi) no geographic information, but remember previously received messages. For each of these network models, we demonstrate localized forwarding algorithms for (based on geography or state information) that achieve significant reductions in the transmission overheads while maintaining hop-delays comparable to flooding based schemes. We also consider the related problem of broadcasting to a set of spatially uniform points in the network (lattice points) in the regime where all nodes have only a local sense of direction and demonstrate an efficient sparse broadcast scheme based on a branching random walk that has a low number of packet transmissions. Thus, our results show that even with very little local information, it is possible to make schemes significantly more efficient.

We consider a finite-field model for the wireless broadcast and additive interference network (WBAIN), both in the presence and absence of fading. We show that the single-source unicast capacity (with extension to multicast) of a WBAIN with or without fading can be upper bounded by the capacity of an equivalent broadcast erasure network. We further present a coding strategy for WBAINs with i.i.d. and uniform fading based on random linear coding at each node that achieves a rate differing from the upper bound by no more than O(1/q), where q is the field size. Using these results, we show that channel fading in conjunction with network coding can lead to large gains in the unicast (multicast) capacity as compared to no fading

In this paper we compare the following two methods of transmit preceding for the multiple antenna broadcast channel: vector perturbation applied to channel inversion (also termed zero forcing or ZF) precoding and scalar Tomlinson-Harashima (TH) precoding applied to sum-rate achieving transmit precoding. Our results indicate that vector perturbation applied to channel inversion preceding can significantly reduce power enhancement and yields the full diversity afforded by the channel to each user. Scalar TH-modulo reduction significantly reduces the power enhancement for precoding based on sum-rate criterion. The solution to vector perturbation applied to ZF precoding requires the solution to an integer optimization problem which is exponentially complex, or an approximation to the integer optimization problem which requires the Lenstra-Lenstra-Lovasz algorithm of polynomial complexity. Instead we propose a simpler solution (an approximation) to the vector perturbation problem based on the Rayleigh-Ritz theorem (R.A. Horn and C.R. Johnson, 1985). This approximate solution achieves the same diversity order as the optimal vector perturbation technique, but suffers a small coding loss. This solution is of polynomial complexity order. Further, a small increase in complexity with a "sphere"-based search around this solution yields significantly better performance. Since this vector perturbation is required to be done at the symbol rate, the lower complexity of the proposed algorithm is valuable in practice

The single-source min-cost multicast problem, which can be framed as a convex optimization problem with the use of network codes and convex increasing edge costs is considered. A decentralized approach to this problem is presented by Lun, Ratnakar for the case where all users cooperate to reach the global minimum. Further, the cost for the scenario where each of the multicast receivers greedily routes its flows is analyzed and the existence of a Nash equilibrium is proved. An allocation rule by which edge cost at each edge is allocated to flows through that edge is presented. We prove that under our pricing rule, the flow cost at user equilibrium is the same as the min-cost. This leads to the construction of a selfish flow-steering algorithm for each receiver, which is also globally optimal. Further, the algorithm is extended for completely distributed flow adaptation at nodes in the network to achieve globally minimal cost in steady state. Analogous results are also presented for the case of multiple multicast sessions

Geographic routing with greedy relaying strategies have been widely studied as a routing scheme in sensor networks. These schemes assume that the nodes have perfect information about the location of the destination. We consider three scenarios: (i) where nodes have location errors (imprecise GPS), (ii) where only coarse geographic information about the destination is available, such as the quadrant or half-plane in which the destination is located, and (iii) where only a small fraction of the nodes have routing information. In this paper, we show that even with such imprecise or limited destination-location information, the routing delays are /spl Theta/(1/M(n)). We further show that routing delays of this magnitude can be obtained even if only a small fraction of the nodes have any location information, and other nodes simply forward the packet to a randomly chosen neighbor, and we validate our analysis with simulation. Finally, we consider the throughput-capacity of networks with progressive routing strategies that take packets closer to the destination in every step, but not necessarily along a straight-line. Such a routing strategy could potentially lead to spatial "hot spots" in the network where many data flows intersect at a spatial region (a node or group of nodes), due to "sub-optimal" routes with increased path-lengths. In this paper, we show that the effect of hot spots due to progressive routing does not reduce the network throughput-capacity in an order sense. In other words, the throughput-capacity with progressive routing is order-wise the same as the maximum achievable throughput-capacity.

For a multiple antenna broadcast channel, the sum-rate capacity achieving transmit strategy requires the centralized transmitter to simultaneously communicate with multiple receivers. The objective of this paper is to design an implementable sum-rate capacity achieving transmit strategy that uses a combination of beamforming and coding for known interference. For a Gaussian broadcast channel with two transmit antennas and two receivers with one antenna each, results indicate that with QAM constellations there is significant gain in sum-rate capacity over an approach that uses only beamforming.

We consider the problem of a user querying for information over a sensor network, where the user does not have prior knowledge of the location of the information. We consider three information query strategies: (i) a source-only search, where the source (user) tries to locate the destination by initiating query which propagates as a continuous time random walk (Brownian motion); (ii) a source and receiver driven "sticky" search, where both the source and the destination send a query or an advertisement (both propagating as random walks), and these leave a "sticky" trail to aid in locating the destination; and (iii) where the destination information is spatially cached (i.e., repeated over space), and the source tries to locate any one of the caches. For a source-only search, we show that the probability that a query is unsuccessful decays as (log (t))-1. When both the source and the destination send queries or advertisements, we show that the probability that a query is unsuccessful decays as t-5/8. Further, faster polynomial decay rates can be achieved by using a finite number of queries or advertisements. Finally, when a spatially periodic cache is employed, we show that the probability that a query is unsuccessful decays no faster than t-1. Thus, we can match the decay rates of the source and the destination driven search with that of a spatial caching strategy by using an appropriate number of queries. This indicates that the appropriate strategy for querying over large sensor networks would be to use multiple queries and advertisements using the "sticky" search strategy.

This paper focuses on congestion control over multi-hop, wireless networks. In a wireless network, an important constraint that arises is that due to the MAC (media access control) layer. Many wireless MACs use a time-division strategy for channel access, where, at any point in space, the physical channel can be accessed by a single user at each instant of time. We develop a fair hop-by-hop congestion control algorithm with the MAC constraint being imposed in the form of a channel access time constraint, using an optimization based framework. In the absence of delay, we show that this algorithm is globally stable using a Lyapunov function based approach. Next, in the presence of delay, we show that the hop-by-hop control algorithm has the property of spatial spreading. In other words, focused loads at a particular spatial location in the network get "smoothed" over space. We derive bounds on the "peak load" at a node, both with hop-by-hop control, as well as with end-to-end control, show that significant gains are achieved with the hop-by-hop scheme, and validate the analytical results with simulation.

Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links, and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the analysis or simulation tractable, often deterministic fluid approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional-differential equations (FDEs). In this paper, we ignore the complexity introduced by the window-based implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionally-fair congestion controllers under a limiting regime where the number of flows in a network is large.

With the rapid growth of Internet, parameter design and analysis for large-scale networks has become a topic of active interest. Since simulation of such large scale systems is not easy, deterministic fluid models have been widely used for both qualitative understanding of the behavior, as well as parameter design for such networks. In this paper, we first study a deterministic fluid model for Internet congestion control when there are multiple TCP-like flows present. We provide conditions under which such a system is globally asymptotically stable in the presence of feedback delay. We then study the corresponding system with the addition of web mice and other nonresponsive flows modeled as stochastic disturbances. We show that, when there are a large number of flows, choosing parameters based on the global stability criterion for the deterministic system (with the noise replaced by its mean value) ensures global stability for the stochastic system as well. Numerical examples and simulation results with some popular active queue management mechanisms validate the parameter choices from analysis. The results indicate that a system with multiple TCP-like flows is globally stable as long as the bandwidth-delay product per flow is not very small.

We consider an unreliable wireless sensor grid-network with n nodes placed in a square of unit area. We are interested in the coverage of the region and the connectivity of the network. We first show that the necessary and sufficient conditions for the random grid network to cover the unit square region as well as ensure that the active nodes are connected are of the form p(n)r2(n) ~ log(n)/n, where r(n) is the transmission radius of each node and p(n) is the probability that a node is "active" (not failed). This result indicates that, when n is large, even if each node is highly unreliable and the transmission power is small, we can still maintain connectivity with coverage. We also show that the diameter of the random grid (i.e., the maximum number of hops required to travel from any active node to another) is of the order √{n/log(n)}. Finally, we derive a sufficient condition for connectivity of the active nodes (without necessarily having coverage). If the node success probability p(n) is small enough, we show that connectivity does not imply coverage.

We consider decentralized congestion control algorithms for low-loss operation of the Internet using the ECN bit. There has been much analysis of such algorithms, but with a few exceptions, these typically ignore the effect of feedback delays in the network on stability. We study a single node with many flows passing through it, with each flow (possibly) having a different round-trip delay. Using a fluid model for the flows, we show that even with delays, the total data rate at the router is bounded; and this bound shows that the (peak) total rate grows linearly with increase in system size, i.e., the fraction of overprovisioning required is constant with respect to N, the number of flows in the system. Further, for typical user data rates and delays seen in the Internet today, the bound is very close to the data rate at the router without delays. Earlier results by Johari and Tan have given conditions for a linearized model of the network to be (locally) stable. We show that even when the linearized model is not stable, the nonlinear model is upper bounded, i.e., the total rate at the bottleneck link is upper bounded, and the upper bound is close to the equilibrium rate for TCP.

Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the simulation tractable, often deterministic fluid model approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations. We justify the use of deterministic models for proportionally fair congestion controllers under a limiting regime where the number of sources in a network is large. We verify our results through simulations of window-based implementations of proportionally fair controllers and TCP.

Motivated by TCP over end-to-end ABR, we study the performance of adaptive window congestion control, when it operates over an explicit feedback rate-control mechanism, in a situation in which the bandwidth available to the elastic traffic is stochastically time varying. It is assumed that the sender and receiver of the adaptive window protocol are colocated with the rate-control endpoints. The objective of the study is to understand if the interaction of the rate-control loop and the window-control loop is beneficial for end-to-end throughput, and how the parameters of the problem (propagation delay, bottleneck buffers, and rate of variation of the available bottleneck bandwidth) affect the performance. The available bottleneck bandwidth is modeled as a two-state Markov chain. We develop an analysis that explicitly models the bottleneck buffers, the delayed explicit rate feedback, and TCP's adaptive window mechanism. The analysis, however, applies only when the variations in the available bandwidth occur over periods larger than the round-trip delay. For fast variations of the bottleneck bandwidth, we provide results from a simulation on a TCP testbed that uses Linux TCP code, and a simulation/emulation of the network model inside the Linux kernel. We find that, over end-to-end ABR, the performance of TCP improves significantly if the network bottleneck bandwidth variations are slow as compared to the round-trip propagation delay. Further, we find that TCP over ABR is relatively insensitive to bottleneck buffer size. These results are for a short-term average link capacity feedback at the ABR level (INSTCAP). We use the testbed to study EFFCAP feedback, which is motivated by the notion of the effective capacity of the bottleneck link. We find that EFFCAP feedback is adaptive to the rate of bandwidth variations at the bottleneck link, and thus yields good performance (as compared to INSTCAP) over a wide range of the rate of bottleneck bandwidth variation. Finally, we study if TCP over ABR, with EFFCAP feedback, provides throughput fairness even if the connections have different round-trip propagation delays.

In this paper, we study discrete-time priority queueing systems fed by a large number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable assumptions on the arrival process to the queue, we show that these asymptotes are the same. We then consider a priority queueing system with two queues. Using the earlier result, we derive an upper bound on the tail probability of the delay. Under certain assumptions on the rate function of the arrival process, we show that the upper bound is tight. We then consider a system with Markovian arrivals and numerically evaluate the delay tail probability and validate these results with simulations.