We investigate a binary classification problem in an edge intelligence system where false negatives are more costly than false positives. The system features a compact, locally deployed model, supplemented by a larger, remote model that is accessible via the network, albeit at an offloading cost. For each sample, our system first uses the locally deployed model for inference. Based on the output of the local model, the sample may be offloaded to the remote model. This work aims to understand the fundamental trade-off between classification accuracy and the offloading costs within such a hierarchical inference (HI) system. To optimise this system, we propose an online learning framework that continuously adapts a pair of thresholds on the local model's confidence scores. These thresholds determine the prediction of the local model and whether a sample is classified locally or offloaded to the remote model. We present a closed-form solution for the setting where the local model is calibrated. For the more general case of uncalibrated models, we introduce H2T2, an online two-threshold hierarchical inference policy, and prove it achieves sublinear regret. H2T2 is model-agnostic, requires no training, and learns during the inference phase using limited feedback. Simulations on real-world datasets show that H2T2 consistently outperforms naive and single-threshold HI policies, sometimes even surpassing single-threshold offline optima. The policy also demonstrates robustness to distribution shifts and adapts effectively to mismatched classifiers.

We study a variant of the experts problem in which new experts are revealed over time according to a stochastic process. The experts are represented by partitions of a hypercube $\mathbb{B}$ in $d$-dimensional Euclidean space. In each round, a point is drawn from $\mathbb{B}$ in an independent and identically distributed manner using an unknown distribution. For each chosen point, we draw $d$ orthogonal hyperplanes parallel to the $d$ faces of $\mathbb{B}$ passing through the point. The set of experts available in a round is the set of partitions of $\mathbb{B}$ created by all the hyperplanes drawn up to that point. Losses are adversarial, and the performance metrics of interest include expected regret and high probability bounds on the sample-path regret. We propose a suitably adapted version of the Hedge algorithm called Hedge-G, which uses a constant learning rate and has $O(\sqrt{2^d T \log T})$ expected regret, which is order-optimal. Further, we show that for Hedge-G, there exists a trade-off between choosing a learning rate that has optimal expected regret and a learning rate that leads to a high probability sample-path regret bound. We address this limitation by proposing AdaHedge-G, a variant of Hedge-G that uses an adaptive learning rate by tracking the loss of the experts revealed up to that round. AdaHedge-G simultaneously achieves $O(\log(\log T)\sqrt{ T \log T})$ expected regret and $O(\log T \sqrt{T \log T})$ sample-path regret, with probability at least $1-T^{-c}$, where $c > 0$ is a constant dependent on $d$.

Hierarchical Inference (HI) has emerged as a promising approach for efficient distributed inference between end devices deployed with small pre-trained Deep Learning (DL) models and edge/cloud servers running large DL models. Under HI, a device uses the local DL model to perform inference on the data samples it collects, and only the data samples on which this inference is likely to be incorrect are offloaded to a remote DL model running on the server. Thus, gauging the likelihood of incorrect local inference is key to implementing HI. A natural approach is to compute a confidence metric for the local DL inference and then use a threshold on this confidence metric to determine whether to offload or not. Recently, the HI online learning problem was studied to learn an optimal threshold for the confidence metric over a sequence of data samples collected over time. However, existing algorithms have computation complexity that grows with the number of rounds and do not exhibit a sub-linear regret bound. In this work, we propose the Hedge-HI algorithm and prove that it has [EQUATION] regret, where T is the number of rounds, and NT is the number of distinct confidence metric values observed till round T. Further, under a mild assumption, we propose Hedge-HI-Restart, which has an [EQUATION] regret bound with high probability and has a much lower computation complexity that grows sub-linearly in the number of rounds. Using runtime measurements on Raspberry Pi, we demonstrate that Hedge-HI-Restart has a runtime lower by order of magnitude and achieves cumulative loss close to that of the alternatives.

We consider the problem of service hosting where a service provider can dynamically rent edge resources via short term contracts to ensure better quality of service to its customers. The service can also be partially hosted at the edge, in which case, customers’ requests can be partially served at the edge. The total cost incurred by the system is modeled as a combination of the rent cost, the service cost incurred due to latency in serving customers, and the fetch cost incurred as a result of the bandwidth used to fetch the code/databases of the service from the cloud servers to host the service at the edge. In this paper, we compare multiple hosting policies with regret as a metric, defined as the difference in the cost incurred by the policy and the optimal policy over some time horizon T. In particular we consider the Retro Renting (RR) and Follow The Perturbed Leader (FTPL) policies proposed in the literature and provide performance guarantees on the regret of these policies. We show that under i.i. d stochastic arrivals, RR policy has linear regret while FTPL policy has constant regret. Next, we propose a variant of FTPL, namely Wait then FTPL (W-FTPL), which also has constant regret while demonstrating much better dependence on the fetch cost. We also show that under adversarial arrivals, RR policy has linear regret while both FTPL and W-FTPL have regret O($\sqrt{T}$) which is orderoptimal.

We consider a system with a single source that measures/tracks a time-varying quantity and periodically attempts to report these measurements to a monitoring station. Each update from the source has to be scheduled on one of$K$available communication channels. The probability of success of each attempted communication is a function of the channel used. This function is unknown to the scheduler. The metric of interest is the Age-of-Information (AoI), formally defined as the time elapsed since the destination received the recent most update from the source. We model our scheduling problem as a variant of the multi-arm bandit problem with communication channels as arms. We characterize a lower bound on the AoI regret achievable by any policy and characterize the performance of UCB, Thompson Sampling, and their variants. Our analytical results show that UCB and Thompson sampling are order-optimal for AoI bandits. In addition, we propose novel policies which, unlike UCB and Thompson Sampling, use the current AoI to make scheduling decisions. Via simulations, we show the proposed AoI-aware policies outperform existing AoI-agnostic policies.

We consider the problem of service hosting where an application provider can dynamically rent edge computing resources and serve user requests from the edge to deliver a better quality of service. A key novelty of this work is that we allow the service to be hosted partially at the edge which enables a fraction of the user query to be served by the edge. We model the total cost for (partially) hosting a service at the edge as a combination of the latency in serving requests, the bandwidth consumption, and the time-varying cost for renting edge resources. We propose an online policy called $\alpha -$RetroRenting $(\alpha -$RR) which dynamically determines the fraction of the service to be hosted at the edge in any time-slot, based on the history of the request arrivals and the rent cost sequence. As our main result, we derive an upper bound on $\alpha -$RR’s competitive ratio with respect to the offline optimal policy that knows the entire request arrival and rent cost sequence in advance. We conduct extensive numerical evaluations to compare the performance of $\alpha -$RR with various benchmarks for synthetic and trace-based request arrival and rent cost processes, and find several parameter regimes where $\alpha -$RR’s ability to store the service partially greatly improves cost-efficiency.

We study a variant of the canonical$k$-center problem over a set of vertices in a metric space, where the underlying distances are apriori unknown. Instead, we can query an oracle which provides noisy/incomplete estimates of the distance between any pair of vertices. We consider two oracle models: Dimension Sampling where each query to the oracle returns the distance between a pair of points in one dimension; and Noisy Distance Sampling where the oracle returns the true distance corrupted by noise. We propose active algorithms, based on ideas such as UCB and Thompson sampling developed in the closely related Multi-Armed Bandit problem, which adaptively decide which queries to send to the oracle and are able to solve the k-center problem within an approximation ratio of two with high probability. We analytically characterize instance-dependent query complexity of our algorithms and also demonstrate significant improvements over naive implementations via numerical evaluations on real-world datasets.

We consider a system composed of a sensor node tracking a time varying quantity. In every discretized time slot, the node attempts to send an update to a central monitoring station through one of K communication channels. We consider the setting where channel realizations are correlated across channels. This is motivated by mmWave based 5G systems where line-of-sight which is critical for successful communication is common across all frequency channels while the effect of other factors like humidity is frequency dependent. The metric of interest is the Age-of-Information (AoI) which is a measure of the freshness of the data available at the monitoring station. In the setting where channel statistics are unknown but stationary across time and correlated across channels, the algorithmic challenge is to determine which channel to use in each time-slot for communication. We model the problem as a Multi-Armed bandit (MAB) with channels as arms. We characterize the fundamental limits on the performance of any policy. In addition, via analysis and simulations, we characterize the performance of variants of the UCB and Thompson Sampling policies that exploit correlation.

Age-of-Information (AoI) is a performance metric for scheduling systems that measures the freshness of the data available at the intended destination. AoI is formally defined as the time elapsed since the destination received the recent most update from the source. We consider the problem of scheduling to minimize the cumulative AoI in a multi-source multi-channel setting. Our focus is on the setting where channel statistics are unknown and we model the problem as a distributed multi-armed bandit problem. For an appropriately defined AoI regret metric, we provide analytical performance guarantees of an existing UCB-based policy for the distributed multi-armed bandit problem. In addition, we propose a novel policy based on Thomson Sampling and a hybrid policy that tries to balance the trade-off between the aforementioned policies. Further, we develop AoI-aware variants of these policies in which each source takes its current AoI into account while making decisions. We compare the performance of various policies via simulations.

We consider a system consisting of a source node which sends updates to a monitoring station using multiple communication channels. These updates are measurements of a time-varying quantity that the source is tracking. The monitoring station uses these updates to make control decisions and therefore needs fresh and accurate updates for optimal performance. One natural way to deal with the case where the updates can be unreliable/noisy is to use multiple recent updates from the source to obtain a robust estimate of the current value of quantity of interest. A recently proposed metric well-suited for this setting is called Loss-of-Credibility (LoC). LoC is a measure of the credibility of the estimate the monitoring station can obtain using the updates it has received.In this work, we focus on the setting each attempted update is successful with a probability which is an unknown function of the channel used for communication. The goal is to design a scheduling algorithm to determine which channel to use to send updates in order to minimize LoC. We model the problem as a multi-arm bandit (MAB) with communication channels as arms and a suitably defined LoC regret metric. We show that UCB and Thompson Sampling are order-optimal for our LoC setting. In addition, we propose variants of these policies which outperform the original policies in simulations.

The Least Recently Used (LRU) policy is widely used in caching, since it is computationally inexpensive and can be implemented ‘on-the-fly.’ However, existing analyses of content- wise hit-rates under LRU have expressions whose complexity grows rapidly with the buffer size. In this paper, we derive a simple yet accurate approximation for the LRU content-wise hitrates under Zipf-distributed requests, in the regime of a large content population. To this end, we map the characteristic time of a content in the LRU policy to the classical Coupon Collector’s Problem (CCP). We justify the accuracy of these approximations by showing analytically that the characteristic time concentrates sharply around its mean. Our bounds highlight and quantify the impact of cache-size scaling as well as the variations in content popularity on the accuracy of the hit-rate estimates. Specifically, we show that these estimates become more accurate with a decrease in Zipf parameter β or an increase in the cache-size scaling. Finally, our analysis of the CCP with Zipf-distributed coupons could be of independent interest.

This work focuses on designing caching policies for transient data, i.e., data which can be used to serve requests only for a finite duration of time after which it becomes redundant. We first characterize the fundamental limit on the performance of caching policies for transient data and characterize the performance of traditional caching policies like LRU for this setting. Traditional caching policies often make decisions based on the popularity of the data being cached. We propose a new caching policy which uses both the popularity and the residual life-time (time remaining before the data becomes redundant) to make caching decisions. We show that in the setting where data being cached is transient, our policy outperforms traditional caching policies.

We study the task of scheduling in a multi-source system where sources report their time-varying information to a central monitoring station via multiple orthogonal channels. The Age-of-Information of a source is defined as the amount of time elapsed since the latest update from that source was received at the monitoring station. At each time instant, the system pays a cost that is a function of the current Ages-of-Information of the sources. Our goal is to design scheduling policies to minimize this cost. We draw a novel parallel between our scheduling problem and the minimum mean cost cycle problem in weighted graphs and use this insight to design optimal scheduling policies for a very general class of cost functions. In addition, we compare the performance of our policy with naive greedy policies. We show that while greedy policies can be optimal if the cost function is symmetric with respect to the sources, our policy strictly outperforms greedy policies when the cost function is asymmetric across sources.

Content delivery networks are a key infrastructure component used by Video on Demand (VoD) services to deliver content over the Internet. We study a content delivery system consisting of a central server and multiple co-located caches, each with limited storage and service capabilities. This work evaluates the performance of such a system as a function of the storage capacity of the caches, the content replication strategy, and the service policy. This analysis can be used for a system-level optimization of these design choices. The focus of this work is on understanding the benefits of allowing caches to pool their resources to serve user requests. We show that the benefits of resource pooling depend on the popularity profile of the contents offered by the VoD service. More specifically, if the popularity does not vary drastically across contents, then resource pooling leads to an order wise reduction in central server transmission rate as the system size grows. On the other hand, if the content popularity is skewed, the central server transmission rate is of the same order with and without resource pooling.

We consider a system consisting of multiple sensors, a central monitoring station, and multiple orthogonal frequency channels. The sensors measure heterogeneous time-varying signals and report their measurements to the central monitoring station which uses them to make control decisions. Due to limited communication capacity, not all sensors can send updates to the monitoring station at all times. The cost the system pays is a function of the weighted sum of the ages-of-information of the various sensors over time. The goal is to design scheduling policies which minimize the time-average of this cost. We propose a policy called SQRT-Weight which fetches updates from sensors at a frequency proportional to the square-root of the corresponding weights and show that this policy is asymptotically 8-optimal. In addition, we compare the performance of the SQRT-Weight policy with other natural scheduling policies via simulations and through analysis for certain special cases.

Motivated by applications like Information Centric Networking for the Internet of Things, we study caching policies for the setting where the data being cached is heterogeneous in nature. This heterogeneity is in two aspects, namely, the lifetime of the data and the size of the data. We propose a caching policy which divides the cache into sub-caches, such that each sub-cache is reserved for data of a specific size and lifetime. Via analytical results and simulations, we show that our policy outperforms existing caching policies for heterogeneous data.

We consider a system consisting of multiple sensors, a central monitoring station, and multiple orthogonal frequency channels. The sensors measure heterogeneous time-varying signals and report their measurements to the central monitoring station which uses them to make control decisions. Due to limited communication capacity, not all sensors can send updates to the monitoring station at all times. The cost of the system pays at any time is a weighted sum of the ages-of-information of the various sensors at that time. The goal is to design scheduling policies which minimize the time-average of this cost. We propose a policy called SQRT-Weight which schedules updates from sensors at a frequency proportional to the square-root of the corresponding weights and show that this policy is asymptotically 8--optimal. In addition, we compare the performance of the SQRT-Weight policy with other natural scheduling policies via simulations.

In this work, we focus on distributed cache systems with non-uniform storage capacity across caches. We compare the performance of our system with the performance of a system with the same cumulative storage distributed evenly across the caches. We characterize the extent to which the performance of the distributed cache system deteriorates due to storage heterogeneity. The key takeaway from this work is that the effects of heterogeneity in the storage capabilities depend heavily on the popularity profile of the contents being cached and delivered. We analytically show that compared to the case where contents popularity is comparable across contents, lopsided popularity profiles are more tolerant to heterogeneity in storage capabilities. We validate our theoretical results via simulations.

We study the caching problem when we are allowed to match each user to one of a subset of caches after its request is revealed. We focus on non-uniformly popular content, specifically when the file popularities obey a Zipf distribution. We study two extremal schemes: one focusing on coded server transmissions while ignoring matching capabilities and the other focusing on adaptive matching while ignoring potential coding opportunities. We derive the rates achieved by these schemes and characterize the regimes in which one outperforms the other. We also compare them to information-theoretic outer bounds and finally propose a hybrid scheme that generalizes ideas from the two schemes and performs at least as well as either of them in most memory regimes.

In this work, we consider a system with multiple sensors, each measuring a different time-varying signal. The sensors report their measurements to a central monitoring station via multiple orthogonal communication channels. An important performance metric in such systems is the age of information at the monitoring station, defined as the amount of time that has elapsed since the recent most update from each sensor. We propose two scheduling policies and prove their optimality with respect to this metric. Another key objective in such systems is to minimize the energy consumption of the sensors. Motivated by this, we propose energy- efficient variants of the two scheduling policies and show that close to optimal performance can be achieved with significant reductions in the energy consumption of the sensors. We provide numerical results to validate our theoretical guarantees.

We study the coded caching problem when we are allowed to match users to caches based on their requested files. We focus on the case where caches are divided into clusters and each user can be assigned to a unique cache from a specific cluster. We show that neither the coded delivery strategy (approximately optimal when the user-cache assignment is pre-fixed) nor the uncoded replication strategy (approximately optimal when all caches belong to a single cluster) is sufficient for all memory regimes. We propose a hybrid solution that combines ideas from both schemes and that performs at least as well as either strategy in most memory regimes. Finally, we show that this hybrid strategy is approximately optimal in most memory regimes.

We study the caching problem when we are allowed to match each user to one of a subset of caches after its request is revealed. We focus on non-uniformly popular content, specifically when the file popularities obey a Zipf distribution. We study two extremal schemes, one focusing on coded server transmissions while ignoring matching capabilities, and the other focusing on adaptive matching while ignoring potential coding opportunities. We derive the rates achieved by these schemes and characterize the regimes in which one outperforms the other. We also compare them to information-theoretic outer bounds, and finally propose for certain cases a hybrid scheme that generalizes ideas from the two schemes and performs at least as well as either of them in most memory regimes.

We consider the task of content replication in distributed content delivery systems used by Video-on-Demand (VoD) services with large content catalogs. The prior work in this area focuses on the setting where each request is generated independent of all past requests. Motivated by the fact that most popular VoD services offer recommendations to users based on their viewing history, in a departure from existing studies, we study the setting where there is time-correlation in requests coming from each user.

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).

Modern content delivery networks consist of one or more "back-end" servers which store the entire content catalog, assisted by multiple "front-end" servers with limited storage and service capacities located near the end-users. Appropriate replication of content on the front-end servers is key to maximize the fraction of requests served by the front-end servers. Motivated by this, a multiple cache variant of the classical single cache paging problem is studied, which is referred to as the Multiple Cache Paging (MCP) problem. In each time-slot, a batch of content requests arrive that have to be served by a bank of caches, and each cache can serve exactly one request. If a content is not found in the bank, it is fetched from the back-end server, and one currently stored content is ejected, and counted as `fault'. As in the classical paging problem, the goal is to minimize the total number of faults. The competitive ratio of any online algorithm for the MCP problem is shown to be unbounded for arbitrary input, thus concluding that the MCP problem is fundamentally different from the classical paging problem. Consequently, stochastic arrivals setting is considered, where requests arrive according to a known/unknown stochastic process. It is shown that near optimal performance can be achieved with simple policies that require no co-ordination across the caches.

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 this paper, we consider the problem of online incentive mechanism design for smart-phone crowd-sourcing. We consider the online setting where users arrive in a sequence and each user participating in crowd-sourcing submits a set of tasks it can accomplish and its corresponding bid. The platform then selects the users and their payments to maximize its utility while ensuring truthfulness, individual rationality, profitability, and polynomial algorithm complexity. The decision whether to accept or reject each user is made instantaneously, with no revocation. We propose an algorithm and show that it satisfies all the four desired properties of an efficient auction. Through extensive simulations, we evaluate the performance of our online algorithm.

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.

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.

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.

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.