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.

We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign, quantization, component-wise and joint clipping. In our work the nonlinearity is treated in a black-box manner, allowing us to establish unified guarantees for a broad range of nonlinear methods. For symmetric noise and non-convex costs we establish convergence of gradient norm-squared, at a rate $\widetilde{\mathcal{O}}(t^{-1/4})$, while for the last iterate of strongly convex costs we establish convergence to the population optima, at a rate $\mathcal{O}(t^{-\zeta})$, where $\zeta \in (0,1)$ depends on noise and problem parameters. Further, if the noise is a (biased) mixture of symmetric and non-symmetric components, we show convergence to a neighbourhood of stationarity, whose size depends on the mixture coefficient, nonlinearity and noise. Compared to state-of-the-art, who only consider clipping and require unbiased noise with bounded $p$-th moments, $p \in (1,2]$, we provide guarantees for a broad class of nonlinearities, without any assumptions on noise moments. While the rate exponents in state-of-the-art depend on noise moments and vanish as $p \rightarrow 1$, our exponents are constant and strictly better whenever $p < 6/5$ for non-convex and $p < 8/7$ for strongly convex costs. Experiments validate our theory, showing that clipping is not always the optimal nonlinearity, further underlining the value of a general framework.

We study a federated version of multi-objective optimization (MOO), where a single model is trained to optimize multiple objective functions. MOO has been extensively studied in the centralized setting but is less explored in federated or distributed settings. We propose FedCMOO, a novel communication-efficient federated multi-objective optimization (FMOO) algorithm that improves the error convergence performance of the model compared to existing approaches. Unlike prior works, the communication cost of FedCMOO does not scale with the number of objectives, as each client sends a single aggregated gradient, obtained using randomized SVD (singular value decomposition), to the central server. We provide a convergence analysis of the proposed method for smooth non-convex objective functions under milder assumptions than in prior work. In addition, we introduce a variant of FedCMOO that allows users to specify a preference over the objectives in terms of a desired ratio of the final objective values. Through extensive experiments, we demonstrate the superiority of our proposed method over baseline approaches.

In cross-device federated learning (FL) with millions of mobile clients, only a small subset of clients participate in training in every communication round, and Federated Averaging (FedAvg) is the most popular algorithm in practice. Existing analyses of FedAvg usually assume the participating clients are independently sampled in each round from a uniform distribution, which does not reflect real-world scenarios. This paper introduces a theoretical framework that models client participation in FL as a Markov chain to study optimization convergence when clients have non-uniform and correlated participation across rounds. We apply this framework to analyze a more practical pattern: every client must wait a minimum number of $R$ rounds (minimum separation) before re-participating. We theoretically prove and empirically observe that increasing minimum separation reduces the bias induced by intrinsic non-uniformity of client availability in cross-device FL systems. Furthermore, we develop an effective debiasing algorithm for FedAvg that provably converges to the unbiased optimal solution under arbitrary minimum separation and unknown client availability distribution.

Federated learning harnesses the power of distributed optimization to train a unified machine learning model across separate clients. However, heterogeneous data distributions and computational workloads can lead to inconsistent updates and limit model performance. This work tackles these challenges by proposing FedECADO, a new algorithm inspired by a dynamical system representation of the federated learning process. FedECADO addresses non-IID data distribution through an aggregate sensitivity model that reflects the amount of data processed by each client. To tackle heterogeneous computing, we design a multi-rate integration method with adaptive step-size selections that synchronizes active client updates in continuous time. Compared to prominent techniques, including FedProx, FedExp, and FedNova, FedECADO achieves higher classification accuracies in numerous heterogeneous scenarios.

Large Language Models (LLMs) have yet to effectively leverage the vast amounts of edge-device data, and Federated Learning (FL) offers a promising paradigm to collaboratively fine-tune LLMs without transferring private edge data to the cloud. To operate within the computational and communication constraints of edge devices, recent literature on federated fine-tuning of LLMs proposes the use of low-rank adaptation (LoRA) and similar parameter-efficient methods. However, LoRA-based methods suffer from accuracy degradation in FL settings, primarily because of data and computational heterogeneity across clients. We propose Ravan, an adaptive multi-head LoRA method that balances parameter efficiency and model expressivity by reparameterizing the weight updates as the sum of multiple LoRA heads, $s_i\textbf{B}_i\textbf{H}_i\textbf{A}_i$, in which only the $\textbf{H}_i$ parameters and their lightweight scaling factors $s_i$ are trained. These trainable scaling factors let the optimization focus on the most useful heads, recovering a higher-rank approximation of the full update without increasing the number of communicated parameters since clients upload $s_i\textbf{H}_i$ directly. Experiments on vision and language benchmarks show that Ravan improves test accuracy by 2–8\% over prior parameter-efficient baselines, making it a robust and scalable solution for federated fine-tuning of LLMs.

In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning, which exhibit a linear speedup with respect to the number of agents and near-optimal dependencies on other salient problem parameters. In the asynchronous setting, existing analyses of federated Q-learning, which adopt an equally weighted averaging of local Q-estimates, require that every agent covers the entire state-action space. In contrast, our improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents to collectively cover the entire state-action space, unveiling the blessing of heterogeneity. However, its sample complexity still suffers when the local trajectories are highly heterogeneous. In response, we propose a novel federated Q-learning algorithm with importance averaging, giving larger weights to more frequently visited state-action pairs, which achieves a robust linear speedup as if all trajectories are centrally processed, regardless of the heterogeneity of local behavior policies.

We consider the problem of efficiently routing jobs that arrive into a central queue to a system of heterogeneous servers. Unlike homogeneous systems, a threshold policy, that routes jobs to the slow server(s) when the queue length exceeds a certain threshold, is known to be optimal for the one-fast-one-slow two-server system. But an optimal policy for the multi-server system is unknown and non-trivial to find. While Reinforcement Learning (RL) has been recognized to have great potential for learning policies in such cases, our problem has an exponentially large state space size, rendering standard RL inefficient. In this work, we propose ACHQ, an efficient policy gradient based algorithm with a low dimensional soft threshold policy parameterization that leverages the underlying queueing structure. We provide stationary-point convergence guarantees for the general case and despite the low-dimensional parameterization prove that ACHQ converges to an approximate global optimum for the special case of two servers. Simulations demonstrate an improvement in expected response time of up to ${\sim}30%$ over the greedy policy that routes to the fastest available server.

Standard federated learning (FL) algorithms typically require multiple rounds of communication between the server and the clients, which has several drawbacks, including requiring constant network connectivity, repeated investment of computational resources, and susceptibility to privacy attacks. One-Shot FL is a new paradigm that aims to address this challenge by enabling the server to train a global model in a single round of communication. In this work, we present FedFisher, a novel algorithm for one-shot FL that makes use of Fisher information matrices computed on local client models, motivated by a Bayesian perspective of FL. First, we theoretically analyze FedFisher for two-layer over-parameterized ReLU neural networks and show that the error of our one-shot FedFisher global model becomes vanishingly small as the width of the neural networks and amount of local training at clients increases. Next, we propose practical variants of FedFisher using the diagonal Fisher and K-FAC approximation for the full Fisher and highlight their communication and compute efficiency for FL. Finally, we conduct extensive experiments on various datasets, which show that these variants of FedFisher consistently improve over competing baselines.

Foundation models (FMs) adapt surprisingly well to downstream tasks with fine-tuning.However, their colossal parameter space prohibits their training on resource-constrained edge-devices.For federated fine-tuning, we need to consider the smaller FMs of few billion parameters at most, namely on-device FMs (ODFMs), which can be deployed ondevice.Federated fine-tuning of ODFMs has unique challenges non-present in standard fine-tuning: i) ODFMs poorly generalize to downstream tasks due to their limited sizes making proper fine-tuning imperative to their performance, and ii) devices have limited and heterogeneous system capabilities and data that can deter the performance of fine-tuning.Tackling these challenges, we propose HET-LORA, a feasible and effective federated finetuning method for ODFMs that leverages the system and data heterogeneity at the edge.HETLORA allows heterogeneous LoRA ranks across clients for their individual system resources, and efficiently aggregates and distributes these LoRA modules in a data-aware manner by applying rank self-pruning locally and sparsity-weighted aggregation at the server.It combines the advantages of high and low-rank LoRAs, achieving improved convergence speed and final performance compared to homogeneous LoRA.Furthermore, HET-LORA has enhanced computation and communication efficiency compared to full finetuning making it more feasible for the edge.

In this paper, we consider a distributed optimization problem. A network of n agents, each with its own local loss function, aims to collaboratively minimize the global average loss. We prove improved convergence results for two recently proposed random reshuffling (RR) based algorithms, D-RR and GT-RR, for smooth strongly-convex and nonconvex problems, respectively. In particular, we prove an additional speedup with increasing n in both cases. Our experiments show that these methods can provide further communication savings by carrying multiple gradient steps between successive communications while also outperforming decentralized SGD. Our experiments also reveal a gap in the theoretical understanding of these methods in the nonconvex case.

Offline reinforcement learning (RL), which seeks to learn an optimal policy using offline data, has garnered significant interest due to its potential in critical applications where online data collection is infeasible or expensive. This work explores the benefit of federated learning for offline RL, aiming at collaboratively leveraging offline datasets at multiple agents. Focusing on finite-horizon episodic tabular Markov decision processes (MDPs), we design FedLCB-Q, a variant of the popular model-free Q-learning algorithm tailored for federated offline RL. FedLCB-Q updates local Q-functions at agents with novel learning rate schedules and aggregates them at a central server using importance averaging and a carefully designed pessimistic penalty term. Our sample complexity analysis reveals that, with appropriately chosen parameters and synchronization schedules, FedLCB-Q achieves linear speedup in terms of the number of agents without requiring high-quality datasets at individual agents, as long as the local datasets collectively cover the state-action space visited by the optimal policy, highlighting the power of collaboration in the federated setting. In fact, the sample complexity almost matches that of the single-agent counterpart, as if all the data are stored at a central location, up to polynomial factors of the horizon length. Furthermore, FedLCB-Q is communication-efficient, where the number of communication rounds is only linear with respect to the horizon length up to logarithmic factors.

Erasure-coded computing has been successfully used in cloud systems to reduce tail latency caused by factors such as straggling servers and heterogeneous traffic variations. A majority of cloud computing traffic now consists of inference on neural networks on shared resources where the response time of inference queries is also adversely affected by the same factors. However, current erasure coding techniques are largely focused on linear computations such as matrix-vector and matrix-matrix multiplications and hence do not work for the highly non-linear neural network functions. In this paper, we seek to design a method to code over neural networks, that is, given two or more neural network models, how to construct a coded model whose output is a linear combination of the outputs of the given neural networks. We formulate the problem as a KL barycenter problem and propose a practical algorithm COIN that leverages the diagonal Fisher information to create a coded model that approximately outputs the desired linear combination of outputs. We conduct experiments to perform erasure coding over neural networks trained on real-world vision datasets and show that the accuracy of the decoded outputs using COIN is significantly higher than other baselines while being extremely compute-efficient.

Federated Learning (FL) enables edge devices or clients to collaboratively train machine learning (ML) models without sharing their private data. Much of the existing work in FL focuses on efficiently learning a model for a single task. In this paper, we study simultaneous training of multiple FL models using a common set of clients. The few existing simultaneous training methods employ synchronous aggregation of client updates, which can cause significant delays because large models and/or slow clients can bottleneck the aggregation. On the other hand, a naive asynchronous aggregation is adversely affected by stale client updates. We propose FedAST, a buffered asynchronous federated simultaneous training algorithm that overcomes bottlenecks from slow models and adaptively allocates client resources across heterogeneous tasks. We provide theoretical convergence guarantees for FedAST for smooth non-convex objective functions. Extensive experiments over multiple real-world datasets demonstrate that our proposed method outperforms existing simultaneous FL approaches, achieving up to 46.0% reduction in time to train multiple tasks to completion.

Federated Learning (FL) under distributed concept drift is a largely unexplored area. Although concept drift is itself a well-studied phenomenon, it poses particular challenges for FL, because drifts arise staggered in time and space (across clients). Our work is the first to explicitly study data heterogeneity in both dimensions. We first demonstrate that prior solutions to drift adaptation, with their single global model, are ill-suited to staggered drifts, necessitating multiple-model solutions. We identify the problem of drift adaptation as a time-varying clustering problem, and we propose two new clustering algorithms for reacting to drifts based on local drift detection and hierarchical clustering. Empirical evaluation shows that our solutions achieve significantly higher accuracy than existing baselines, and are comparable to an idealized algorithm with oracle knowledge of the ground-truth clustering of clients to concepts at each time step.

Many existing FL methods assume clients with fully-labeled data, while in realistic settings, clients have limited labels due to the expensive and laborious process of labeling. Limited labeled local data of the clients often leads to their local model having poor generalization abilities to their larger unlabeled local data, such as having class-distribution mismatch with the unlabeled data. As a result, clients may instead look to benefit from the global model trained across clients to leverage their unlabeled data, but this also becomes difficult due to data heterogeneity across clients. In our work, we propose FedLabel where clients selectively choose the local or global model to pseudo-label their unlabeled data depending on which is more of an expert of the data. We further utilize both the local and global models’ knowledge via global-local consistency regularization which minimizes the divergence between the two models’ outputs when they have identical pseudo-labels for the unlabeled data. Unlike other semi-supervised FL baselines, our method does not require additional experts other than the local or global model, nor require additional parameters to be communicated. We also do not assume any server-labeled data or fully labeled clients. For both cross-device and cross-silo settings, we show that FedLabel outperforms other semi-supervised FL baselines by 8-24%, and even outperforms standard fully supervised FL baselines (100% labeled data) with only 5-20% of labeled data.

Federated Averaging (FedAvg) and its variants are the most popular optimization algorithms in federated learning (FL). Previous convergence analyses of FedAvg either assume full client participation or partial client participation where the clients can be uniformly sampled. However, in practical cross-device FL systems, only a subset of clients that satisfy local criteria such as battery status, network connectivity, and maximum participation frequency requirements (to ensure privacy) are available for training at a given time. As a result, client availability follows a *natural cyclic pattern*. We provide (to our knowledge) the first theoretical framework to analyze the convergence of FedAvg with cyclic client participation with several different client optimizers such as GD, SGD, and shuffled SGD. Our analysis discovers that cyclic client participation can achieve a faster asymptotic convergence rate than vanilla FedAvg with uniform client participation under suitable conditions, providing valuable insights into the design of client sampling protocols.

In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and sharper dependencies on other salient problem parameters. Moreover, existing approaches to federated Q-learning adopt an equally-weighted averaging of local Q-estimates, which can be highly sub-optimal in the asynchronous setting since the local trajectories can be highly heterogeneous due to different local behavior policies. Existing sample complexity scales inverse proportionally to the minimum entry of the stationary state-action occupancy distributions over all agents, requiring that every agent covers the entire state-action space. Instead, we propose a novel importance averaging algorithm, giving larger weights to more frequently visited state-action pairs. The improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents collectively cover the entire state-action space, unveiling the blessing of heterogeneity.

We study the problem of communication-efficient distributed vector mean estimation, which is a commonly used subroutine in distributed optimization and Federated Learning (FL). Rand-$k$ sparsification is a commonly used technique to reduce communication cost, where each client sends $k < d$ of its coordinates to the server. However, Rand-$k$ is agnostic to any correlations, that might exist between clients in practical scenarios. The recently proposed Rand-$k$-Spatial estimator leverages the cross-client correlation information at the server to improve Rand-$k$'s performance. Yet, the performance of Rand-$k$-Spatial is suboptimal, and improving mean estimation is key to a faster convergence in distributed optimization. We propose the Rand-Proj-Spatial estimator with a more flexible encoding-decoding procedure, which generalizes the encoding of Rand-$k$ by projecting the client vectors to a random $k$-dimensional subspace. We utilize Subsampled Randomized Hadamard Transform (SRHT) as the projection matrix, and show that Rand-Proj-Spatial with SRHT outperforms Rand-$k$-Spatial, using the correlation information more efficiently. Furthermore, we propose an approach to incorporate varying degrees of correlation, and suggest a practical variant of Rand-Proj-Spatial when the correlation information is not available to the server. Finally, experiments on real-world distributed optimization tasks showcase the superior performance of Rand-Proj-Spatial compared to Rand-$k$-Spatial and other more sophisticated sparsification techniques.

Federated learning is a distributed optimization paradigm that enables a large number of resource-limited client nodes to cooperatively train a model without data sharing. Previous works analyzed the convergence of federated learning by accounting of data heterogeneity, communication/computation limitations, and partial client participation. However, most assume unbiased client participation, where clients are selected such that the aggregated model update is unbiased. In our work, we present the convergence analysis of federated learning with biased client selection and quantify how the bias affects convergence speed. We show that biasing client selection towards clients with higher local loss yields faster error convergence. From this insight, we propose Power-of-Choice, a communication- and computation-efficient client selection framework that flexibly spans the trade-off between convergence speed and solution bias. Extensive experiments demonstrate that Power-of-Choice can converge up to 3 times faster and give $10%$ higher test accuracy than the baseline random selection.

Federated learning is an emerging machine learning framework where models are trained using heterogeneous datasets collected by a large number of edge clients. Standard methods to aggregate local training models weigh each model by a fraction of data size at that client. However, such approaches result in unfairness to clients with small and unique datasets, leading to inferior accuracy of the global model at these clients. In this work, we propose a novel optimization framework called DRFL that dynamically adjusts the weight assigned to each client, and we combine it with a biased client selection strategy, both of which encourage fairness in federated training. We validate the effectiveness of our proposed method on a suite of both synthetic and real federated datasets, revealing the proposed method outperforms existing baselines in terms of resulting fairness.

Since reinforcement learning algorithms are notoriously data-intensive, the task of sampling observations from the environment is usually split across multiple agents. However, transferring these observations from the agents to a central location can be prohibitively expensive in terms of the communication cost, and it can also compromise the privacy of each agent’s local behavior policy. In this paper, we consider a federated reinforcement learning framework where multiple agents collaboratively learn a global model, without sharing their individual data and policies. Each agent maintains a local copy of the model and updates it using locally sampled data. Although having N agents enables the sampling of N times more data, it is not clear if it leads to proportional convergence speedup. We propose federated versions of on-policy TD, off-policy TD and Q-learning, and analyze their convergence. For all these algorithms, to the best of our knowledge, we are the first to consider Markovian noise and multiple local updates, and prove a linear convergence speedup with respect to the number of agents. To obtain these results, we show that federated TD and Q-learning are special cases of a general framework for federated stochastic approximation with Markovian noise, and we leverage this framework to provide a unified convergence analysis that applies to all the algorithms.

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications, such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has order-optimal sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys linear speedup with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.

Federated learning (FL) enables edge-devices to collaboratively learn a model without disclosing their private data to a central aggregating server. Most existing FL algorithms require models of identical architecture to be deployed across the clients and server, making it infeasible to train large models due to clients' limited system resources. In this work, we propose a novel ensemble knowledge transfer method named Fed-ET in which small models (different in architecture) are trained on clients, and used to train a larger model at the server. Unlike in conventional ensemble learning, in FL the ensemble can be trained on clients' highly heterogeneous data. Cognizant of this property, Fed-ET uses a weighted consensus distillation scheme with diversity regularization that efficiently extracts reliable consensus from the ensemble while improving generalization by exploiting the diversity within the ensemble. We show the generalization bound for the ensemble of weighted models trained on heterogeneous datasets that supports the intuition of Fed-ET. Our experiments on image and language tasks show that Fed-ET significantly outperforms other state-of-the-art FL algorithms with fewer communicated parameters, and is also robust against high data-heterogeneity.

We address the problem of slowdown caused by straggling nodes in distributed non-linear computations. Many common non-linear computations can be written as a sum of inexpensive non-linear functions (e.g. Taylor series). Based on this observation, we propose a new class of rateless codes called rateless sum-recovery codes whose aim is to recover the sum of source symbols, without necessarily recovering individual symbols. Source symbols correspond to individual inexpensive functions and each encoded symbol is the sum of a subset of source symbols. Encoded symbols are computed in a distributed fashion and for a computation that can be written as a sum of m inexpensive functions, successful sum-recovery is possible with high probability as long as slightly more than m encoded symbols are received. Our code is rateless, systematic and has sparse parities. Moreover, encoded symbols are constructed by sampling without replacement at individual nodes, thereby making decoding superfluous if the encoded symbols from any node cover all source symbols. We validate our claims through a range of simulations and also discuss open questions for future works.A full version of this paper is accessible at [1].

Most data generated by modern applications is stored in the cloud, and there is an exponential growth in the volume of jobs to access these data and perform computations using them. The volume of data access or computing jobs can be heterogeneous across different job types and can unpredictably change over time. Cloud service providers cope with this demand heterogeneity and unpredictability by over-provisioning the number of servers hosting each job type. In this paper, we propose the addition of erasure-coded servers that can flexibly serve multiple job types without additional storage cost. We analyze the service capacity region and the response time of such erasure-coded systems and compare them with standard uncoded replication-based systems currently used in the cloud. We show that coding expands the service capacity region, thus enabling the system to handle variability in demand for different data types. Moreover, we characterize the response time of the coded system in various arrival rate regimes. This analysis reveals that adding even a small number of coded servers can significantly reduce the mean response time, with a drastic reduction in regimes where the demand is skewed across different job types.

We study a sequential resource allocation problem where, at each round, the decision-maker needs to allocate its limited budget among different available entities. In doing so, the decision-maker obtains the reward for each entity in that round. The goal of the decision-maker is to maximize the expected cumulative reward or equivalently minimize cumulative regret over a total of T rounds. Sequential resource allocation can be modeled as a combinatorial bandit by viewing the allocation of a budget to an entity as a base arm. In the context of resource allocation, the rewards received under different budget allocations are likely to be correlated. We propose a novel correlated combinatorial bandit framework that explicitly models such correlations. We develop a novel Correlated-UCB algorithm for online resource allocation, which yields significantly reduced regret relative to correlation-agnostic algorithms. In certain cases, our proposed algorithm even achieves bounded regret, which is an order-wise reduction in the regret relative to the correlation-agnostic approach, which incurs logarithmic regret under all scenarios. We validate these performance gains through experiments on several applications such as online power allocation across wireless channels, job scheduling in multi-server systems and online channel assignment for the slotted ALOHA protocol.

Data-heterogeneous federated learning (FL) systems suffer from two significant sources of convergence error: 1) client drift error caused by performing multiple local optimization steps at clients, and 2) partial client participation error caused by the fact that only a small subset of the edge clients participate in every training round. We find that among these, only the former has received significant attention in the literature. To remedy this, we propose FedVARP, a novel variance reduction algorithm applied at the server that eliminates error due to partial client participation. To do so, the server simply maintains in memory the most recent update for each client and uses these as surrogate updates for the non-participating clients in every round. Further, to alleviate the memory requirement at the server, we propose a novel clustering-based variance reduction algorithm ClusterFedVARP. Unlike previously proposed methods, both FedVARP and ClusterFedVARP do not require additional computation at clients or communication of additional optimization parameters. Through extensive experiments, we show that FedVARP outperforms state-of-the-art methods, and ClusterFedVARP achieves performance comparable to FedVARP with much less memory requirements.

Due to the massive size of the neural network models and training datasets used in machine learning today, it is imperative to distribute stochastic gradient descent (SGD) by splitting up tasks such as gradient evaluation across multiple worker nodes. However, running distributed SGD can be prohibitively expensive because it may require specialized computing resources such as GPUs for extended periods of time. We propose cost-effective strategies to exploit volatile cloud instances that are cheaper than standard instances, but may be interrupted by higher priority workloads. To the best of our knowledge, this work is the first to quantify how variations in the number of active worker nodes (as a result of preemption) affect SGD convergence and the time to train the model. By understanding these trade-offs between preemption probability of the instances, accuracy, and training time, we are able to derive practical strategies for configuring distributed SGD jobs on volatile instances such as Amazon EC2 spot instances and other preemptible cloud instances. Experimental results show that our strategies achieve good training performance at substantially lower cost.

We consider a finite-armed structured bandit problem in which mean rewards of different arms are known functions of a common hidden parameter θ*. This problem setting subsumes several previously studied frameworks that assume linear or invertible reward functions. We propose a novel approach to gradually estimate the hidden θ*and use the estimate together with the mean reward functions to substantially reduce exploration of sub-optimal arms. This approach enables us to fundamentally generalize any classic bandit algorithm including UCB and Thompson Sampling to the structured bandit setting. We prove via regret analysis that our proposed UCB-C and TS-C algorithms (structured bandit versions of UCB and Thompson Sampling, respectively) pull only a subset of the sub-optimal arms O(log T ) times while the other sub-optimal arms (referred to as non-competitive arms) are pulled O(1) times. As a result, in cases where all sub-optimal arms are noncompetitive, which can happen in many practical scenarios, the proposed algorithms achieve bounded regret.

Communication of model updates between client nodes and the central aggregating server is a major bottleneck in federated learning, especially in bandwidth-limited settings and high-dimensional models. Gradient quantization is an effective way of reducing the number of bits required to communicate each model update, albeit at the cost of having a higher error floor due to the higher variance of the stochastic gradients. In this work, we propose an adaptive quantization strategy called AdaQuantFL that aims to achieve communication efficiency as well as a low error floor by changing the number of quantization levels during the course of training. Experiments on training deep neural networks show that our method can converge in much fewer communicated bits as compared to fixed quantization level setups, with little or no impact on training and test accuracy.

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.

We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be prohibitive, and it may be imperative for them to use sparsification techniques. While most existing work on sparsified mean estimation is agnostic to the characteristics of the data vectors, in many practical applications such as federated learning, there may be spatial correlations (similarities in the vectors sent by different nodes) or temporal correlations (similarities in the data sent by a single node over different iterations of the algorithm) in the data vectors. We leverage these correlations by simply modifying the decoding method used by the server to estimate the mean. We provide an analysis of the resulting estimation error as well as experiments for PCA, K-Means and Logistic Regression, which show that our estimators consistently outperform more sophisticated and expensive sparsification methods.

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels are not very effective at capturing similarity between high dimensional data points. Neural networks can be used to learn good representations that encode intricate structures in high dimensional data, and can be used as inputs to the GP kernel. However the huge data requirement of neural networks makes this approach ineffective in small data settings. To solves the conflicting problems of representation learning and data efficiency, we propose to learn deep kernels on probabilistic embeddings by using a probabilistic neural network. Our approach maps high-dimensional data to a probability distribution in a low dimensional subspace and then computes a kernel between these distributions to capture similarity. To enable end-to-end learning, we derive a functional gradient descent procedure for training the model. Experiments on a variety of datasets show that our approach outperforms the state-of-the-art in GP kernel learning in both supervised and semi-supervised settings. We also extend our approach to other small-data paradigms such as few-shot classification where it outperforms previous approaches on mini-Imagenet and CUB datasets.

When training machine learning models using stochastic gradient descent (SGD) with a large number of nodes or massive edge devices, the communication cost of synchronizing gradients at every iteration is a key bottleneck that limits the scalability of the system and hinders the benefit of parallel computation. Local-update SGD algorithms, where worker nodes perform local iterations of SGD and periodically synchronize their local models, can effectively reduce the communication frequency and save the communication delay. In this paper, we propose a powerful framework, named Cooperative SGD, that subsumes a variety of local-update SGD algorithms (such as local SGD, elastic averaging SGD, and decentralized parallel SGD) and provides a unified convergence analysis. Notably, special cases of the unified convergence analysis provided by the cooperative SGD framework yield 1) the first convergence analysis of elastic averaging SGD for general non-convex objectives, and 2) improvements upon previous analyses of local SGD and decentralized parallel SGD. Moreover, we design new algorithms such as elastic averaging SGD with overlapped computation and communication, and decentralized periodic averaging which are shown to be 4x or more faster than the baseline in reaching the same training loss.

Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding can help boost theservice rate region, that is, increase the overall volume of data access requests that the system can handle. This paper aims to postulate the service rate region as an important consideration in the design of erasure-coded distributed systems. We highlight several open problems that can be grouped into two broad threads: 1) characterizing the service rate region of a given code and finding the optimal request allocation, and 2) designing the underlying erasure code for a given service rate region. As contributions along the first thread, we find the rate regions of maximum-distance-separable, locally repairable, and simplex codes. We show the effectiveness of hybrid codes that combine replication and erasure coding in terms of code design. We also discover fundamental connections between multi-set batch codes and the problem of maximizing the service rate region.

We consider a multi-armed bandit framework where the rewards obtained by pulling different arms are correlated. We develop a unified approach to leverage these reward correlations and present fundamental generalizations of classic bandit algorithms to the correlated setting. We present a unified proof technique to analyze the proposed algorithms. Rigorous analysis of C-UCB (the correlated bandit versions of Upper-confidence-bound) reveals that the algorithm end up pulling certain sub-optimal arms, termed as non-competitive, only O(1) times, as opposed to the O(logT) pulls required by classic bandit algorithms such as UCB, TS etc. We present regret-lower bound and show that when arms are correlated through a latent random source, our algorithms obtain order-optimal regret. We validate the proposed algorithms via experiments on the MovieLens and Goodreads datasets, and show significant improvement over classical bandit algorithms.

The maximum possible throughput (or the rate of job completion) of a multi-server system is typically the sum of the service rates of individual servers. Recent work shows that launching multiple replicas of a job and canceling them as soon as one copy finishes can boost the throughput, especially when the service time distribution has high variability. This means that redundancy can, in fact, create synergy among servers such that their overall throughput is greater than the sum of individual servers. This work seeks to find the fundamental limit of the throughput boost achieved by job replication and the optimal replication policy to achieve it. While most previous works consider upfront replication policies, we expand the set of possible policies to delayed launch of replicas. The search for the optimal adaptive replication policy can be formulated as a Markov Decision Process, using which we propose two myopic replication policies, MaxRate and AdaRep, to adaptively replicate jobs. In order to quantify the optimality gap of these and other policies, we derive upper bounds on the service capacity, which provide fundamental limits on the throughput of queueing systems with redundancy.

Multi-armed bandit models are widely studied sequential decision-making problems that exemplify the exploration-exploitation trade-off. We study a novel correlated multi-armed bandit model where the rewards obtained from the arms are functions of a common latent random variable. We propose and analyze the performance of the C-UCB algorithm that leverages the correlations between arms to reduce the cumulative regret (i.e., to increase the total reward obtained after T rounds). Unlike the standard UCB algorithm that pulls all sub-optimal arms O(log T) times, the C-UCB algorithm takes only O(1) times to identify that some arms, which we refer to as non-competitive arms, are optimal. Thus, we effectively reduce a K-armed bandit problem to a C + 1-armed bandit problem with C <; K denoting the number of competitive, where C can be computed from the reward functions. A key consequence is that when C = 0, our algorithm achieves a constant (i.e., O(1)) regret instead of the standard O(log T) scaling with the number of rounds T . Establishing lower bounds for the regret, we show that the C-UCB algorithm is order-wise optimal and demonstrate its superiority against other algorithms via numerical simulations.

Distributed stochastic gradient descent (SGD) is essential for scaling the machine learning algorithms to a large number of computing nodes. However, the infrastructures variability such as high communication delay or random node slowdown greatly impedes the performance of distributed SGD algorithm, especially in a wireless system or sensor networks. In this paper, we propose an algorithmic approach named Overlap Local-SGD (and its momentum variant) to overlap communication and computation so as to speedup the distributed training procedure. The approach can help to mitigate the straggler effects as well. We achieve this by adding an anchor model on each node. After multiple local updates, locally trained models will be pulled back towards the synchronized anchor model rather than communicating with others. Experimental results of training a deep neural network on CIFAR-10 dataset demonstrate the effectiveness of Overlap Local-SGD. We also provide a convergence guarantee for the proposed algorithm under non-convex objective functions.A full version of this paper with additional examples and proofs is accessible at: http://andrew.cmu.edu/user/gaurij/overlap_local_SGD.pdf.

Due to the massive size of the neural network models and training datasets used in machine learning today, it is imperative to distribute stochastic gradient descent (SGD) by splitting up tasks such as gradient evaluation across multiple worker nodes. However, running distributed SGD can be prohibitively expensive because it may require specialized computing resources such as GPUs for extended periods of time. We propose cost-effective strategies to exploit volatile cloud instances that are cheaper than standard instances, but may be interrupted by higher priority workloads. To the best of our knowledge, this work is the first to quantify how variations in the number of active worker nodes (as a result of preemption) affects SGD convergence and the time to train the model. By understanding these trade-offs between preemption probability of the instances, accuracy, and training time, we are able to derive practical strategies for configuring distributed SGD jobs on volatile instances such as Amazon EC2 spot instances and other preemptible cloud instances. Experimental results show that our strategies achieve good training performance at substantially lower cost.

In federated learning, heterogeneity in the clients' local datasets and computation speeds results in large variations in the number of local updates performed by each client in each communication round. Naive weighted aggregation of such models causes objective inconsistency, that is, the global model converges to a stationary point of a mismatched objective function which can be arbitrarily different from the true objective. This paper provides a general framework to analyze the convergence of federated heterogeneous optimization algorithms. It subsumes previously proposed methods such as FedAvg and FedProx and provides the first principled understanding of the solution bias and the convergence slowdown due to objective inconsistency. Using insights from this analysis, we propose FedNova, a normalized averaging method that eliminates objective inconsistency while preserving fast error convergence.

We propose a rateless fountain coding strategy to alleviate the problem of straggling nodes - computing nodes that unpredictably slowdown or fail - in distributed matrix-vector multiplication. Our algorithm generates linear combinations of the m rows of the matrix, and assigns them to different worker nodes, which then perform row-vector products with the encoded rows. The original matrix-vector product can be decoded as soon as slightly more than m row-vector products are collectively completed by the nodes. This strategy enables fast nodes to steal work from slow nodes, without requiring the knowledge of node speeds. Compared to recently proposed fixed-rate erasure coding strategies which ignore partial work done by straggling nodes, rateless codes have a significantly lower overall delay, and a smaller computational overhead.

Unpredictable slowdown of worker nodes, or node straggling, is a major bottleneck when performing large matrix computations such as matrix-vector multiplication in a distributed fashion. For sparse matrices, the problem is compounded by irregularities in the distribution of non-zero elements, which leads to an imbalance in the computation load at different nodes. To mitigate the effect of stragglers we use rateless codes that generate redundant linear combinations of the matrix rows (or columns) and distribute them across workers. This coding scheme utilizes all partial work done by worker nodes, and eliminates tail latency. We also propose a balanced row-allocation strategy for allocating rows of a sparse matrix to workers that ensures that equal amount of non-zero matrix entries are assigned to each worker. The entire scheme is designed to work with compressed, memory-efficient formats like CSR/CSC that are used to store sparse matrices in practice. Theoretical analysis and simulations show that our balanced rateless coding strategy achieves significantly lower overall latency than conventional sparse matrix-vector multiplication strategies.

Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in waiting for the slowest learners (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect convergence. In this work we present the first theoretical characterization of the speed-up offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime (wallclock time). The novelty in our work is that our runtime analysis considers random straggler delays, which helps us design and compare distributed SGD algorithms that strike a balance between stragglers and staleness. We also present a new convergence analysis of asynchronous SGD variants without bounded or exponential delay assumptions, and a novel learning rate schedule to compensate for gradient staleness.

We consider storage systems in which K files are stored over N nodes. A node may be systematic for a particular file in the sense that access to it gives access to the file. Alternatively, a node may be coded, meaning that it gives access to a particular file only when combined with other nodes (which may be coded or systematic). Requests for file fkarrive at rate λk, and we are interested in the rate that can be served by a particular system. In this paper, we determine the set of request arrival rates for the a 3-file coded storage system. We also provide an algorithm to maximize the rate of requests served for file K given λ1, . . . , λK-1in a general K-file case.

We consider a streaming communication system where the source packets must be played back sequentially at the destination and study the associated average playback delay. We assume that all the source packets are available before the start of transmission at the transmitter and consider the case of an i.i.d. erasure channel with perfect feedback. We first consider the case when the receiver buffer can be arbitrarily large, and show that the average playback delay remains bounded in the length of the stream provided that the channel bandwidth is greater than a critical threshold. Our analysis involves the application of martingale theory to study the transient behaviour of a one dimensional random walk with drift. Conversely when the channel bandwidth is smaller than the above threshold, the average playback delay increases linearly with the stream length. We also consider the finite buffer case and analyse the playback delay of a greedy dynamic bandwidth scheme. We further show through simulations that the achievable delay with a finite receiver buffer is close to the infinite buffer case for moderately large buffer values.

Large-scale distributed computing systems divide a job into many independent tasks and run them in parallel on different machines. A challenge in such parallel computing is that the time taken by a machine to execute a task is inherently variable, and thus the slowest machine becomes the bottleneck in the completion of the job. One way to combat the variability in machine response is to replicate tasks on multiple machines and waiting for the machine that finishes first. While task replication reduces response time, it generally increases resource usage. In this work, we propose a theoretical framework to analyze the trade-off between response time and resource usage. Given an execution time distribution for machines, our analysis gives insights on when and why replication helps. We also propose efficient scheduling algorithms for large-scale distributed computing systems.

We study how coding in distributed storage reduces expected download time, in addition to providing reliability against disk failures. The expected download time is reduced because when a content file is encoded with redundancy and distributed across multiple disks, reading only a subset of the disks is sufficient for content reconstruction. For the same total storage used, coding exploits the diversity in storage better than simple replication, and hence gives faster download. We use a novel fork-join queueing framework to model multiple users requesting the content simultaneously, and derive bounds on the expected download time. Our system model and results are a novel generalization of the fork-join system that is studied in queueing theory literature. Our results demonstrate the fundamental trade-off between the expected download time and the amount of storage space. This trade-off can be used for design of the amount of redundancy required to meet the delay constraints on content delivery.

We analyze the download time of a large file, divided into chunks called generations, and transmitted over an erasure channel without feedback. For non-overlapping generations, we derive how the download time scales with the number of generations, for the round-robin and random scheduling policies. We then analyze coding with overlapping generations and show that the optimal overlap size is small compared to the number of generations, which implies that the download time can be reduced with only a small increase in computational complexity. Further, for a given overlap size, we propose overlap structures that have low complexity and are easy to implement, but still give file download as fast as the best previously proposed structures.

We consider the problem of minimizing playback delay in streaming over a packet erasure channel with fixed bandwidth. When packets have to be played in order, the expected delay inherently grows with time. We analyze two cases, namely no feedback and instantaneous feedback. We find that in both cases the delay grows logarithmically with the time elapsed since the start of transmission, and we evaluate the growth constant, i.e. the pre-log term, as a function of the transmission bandwidth (relative to the source bandwidth). The growth constant with feedback is strictly better that the one without, but they have the same asymptotic value in the limit of infinite bandwidth.