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We study the smoothed online quadratic optimization (SOQO) problem where, at each round t, a player plays an action xt in response to a quadratic hitting cost and an additional squared ℓ2-norm cost for switching actions. This problem class has strong connections to a wide range of application domains including smart grid management, adaptive control, and data center management, where switching-efficient algorithms are highly sought after. We study the SOQO problem in both adversarial and stochastic settings, and in this process, perform the first stochastic analysis of this class of problems. We provide the online optimal algorithm when the minimizers of the hitting cost function evolve as a general stochastic process, which, for the case of martingale process, takes the form of a distribution-agnostic dynamic interpolation algorithm that we call Lazy Adaptive Interpolation (LAI). Next, we present the stochastic-adversarial trade-off by proving an Ω(T) expected regret for the adversarial optimal algorithm in the literature (ROBD) with respect to LAI and, a sub-optimal competitive ratio for LAI in the adversarial setting. Finally, we present a best-of-both-worlds algorithm that obtains a robust adversarial performance while simultaneously achieving a near-optimal stochastic performance. 

We consider a large-scale parallel-server loss system with an unknown arrival rate, where each server is able to adjust its processing speed. The objective is to minimize the system cost, which consists of a power cost to maintain the servers' processing speeds and a quality of service cost depending on the tasks' processing times, among others. We draw on ideas from stochastic approximation to design a novel speed scaling algorithm and prove that the servers' processing speeds converge to the globally asymptotically optimum value. Curiously, the algorithm is fully distributed and does not require any communication between servers. Apart from the algorithm design, a key contribution of our approach lies in demonstrating how concepts from the stochastic approximation literature can be leveraged to effectively tackle learning problems in large-scale, distributed systems. En route, we also analyze the performance of a fully heterogeneous parallel-server loss system, where each server has a distinct processing speed, which might be of independent interest. 

We consider large-scale load balancing systems where processing time distribution of tasks depend on both task and server types. We analyze the system in the asymptotic regime where the number of task and server types tend to infinity proportionally to each other. In such heterogeneous setting, popular policies like Join Fastest Idle Queue (JFIQ), Join Fastest Shortest Queue (JFSQ) are known to perform poorly and they even shrink the stability region. Moreover, to the best of our knowledge, in this setup, finding a scalable policy with provable performance guarantee has been an open question prior to this work. In this paper, we propose and analyze two asymptotically delay-optimal dynamic load balancing approaches: (a) one that efficiently reserves the processing capacity of each server for good tasks and route tasks under the Join Idle Queue policy; and (b) a speed-priority policy that increases the probability of servers processing tasks at a high speed. Introducing a novel analytical framework and using the mean-field method and stochastic coupling arguments, we prove that both policies above achieve asymptotic zero queueing, whereby the probability that a typical task is assigned to an idle server tends to 1 as the system scales. 

We consider load balancing in large-scale heterogeneous server systems in the presence of data locality that imposes constraints on which tasks can be assigned to which servers. The constraints are naturally captured by a bipartite graph between the servers and the dispatchers handling assignments of various arrival flows. When a task arrives, the corresponding dispatcher assigns it to a server with the shortest queue among [Formula: see text] randomly selected servers obeying these constraints. Server processing speeds are heterogeneous, and they depend on the server type. For a broad class of bipartite graphs, we characterize the limit of the appropriately scaled occupancy process, both on the process level and in steady state, as the system size becomes large. Using such a characterization, we show that imposing data locality constraints can significantly improve the performance of heterogeneous systems. This is in stark contrast to either heterogeneous servers in a full flexible system or data locality constraints in systems with homogeneous servers, both of which have been observed to degrade the system performance. Extensive numerical experiments corroborate the theoretical results. Funding: This work was partially supported by the National Science Foundation [CCF. 07/2021–06/2024]. 

Modern data centers suffer from immense power consumption. As a result, data center operators have heavily invested in capacity-scaling solutions, which dynamically deactivate servers if the demand is low and activate them again when the workload increases. We analyze a continuous-time model for capacity scaling, where the goal is to minimize the weighted sum of flow time, switching cost, and power consumption in an online fashion. We propose a novel algorithm, called adaptive balanced capacity scaling (ABCS), that has access to black-box machine learning predictions. ABCS aims to adapt to the predictions and is also robust against unpredictable surges in the workload. In particular, we prove that ABCS is [Formula: see text] competitive if the predictions are accurate, and yet, it has a uniformly bounded competitive ratio even if the predictions are completely inaccurate. Finally, we investigate the performance of this algorithm on a real-world data set and carry out extensive numerical experiments, which positively support the theoretical results. Funding: This work was partially supported by the Division of Computing and Communication Foundations [Grant 2113027]. The authors also acknowledge financial support for this project from the Algorithm and Randomness Center–Transdisciplinary Research Institute for Advancing Data Science Fellowship at Georgia Tech.