Independent learning (IL) is a popular approach for achieving scalability in large-scale multi-agent systems, yet it typically lacks global convergence guarantees. In this paper, we study two representative algorithms—independent $Q$-learning and independent natural actor-critic—within both value-based and policy-based frameworks, and provide the first finite-sample analysis for approximate global convergence. Our results show that IL can achieve global convergence up to a fixed error arising from agent interdependence, which characterizes the fundamental limit of IL in achieving true global convergence. To establish these results, we develop a novel approach by constructing a separable Markov decision process (MDP) for convergence analysis and then bounding the gap caused by the model discrepancy between this separable MDP and the original one. Finally, we present numerical experiments using a synthetic MDP and an electric vehicle charging example to demonstrate our findings and the practical applicability of IL.

Online reinforcement learning (RL) typically requires online interaction data to learn a policy for a target task, but collecting such data can be high-stakes. This prompts interest in leveraging historical data to improve sample efficiency. The historical data may come from outdated or related source environments with different dynamics. It remains unclear how to effectively use such data in the target task to provably enhance learning and sample efficiency. To address this, we propose a hybrid transfer RL (HTRL) setting, where an agent learns in a target environment while accessing offline data from a source environment with shifted dynamics. We show that – without information on the dynamics shift – general shifted-dynamics data, even with subtle shifts, does not reduce sample complexity in the target environment. However, focusing on HTRL with prior information on the degree of the dynamics shift, we design HySRL, a transfer algorithm that outperforms pure online RL with problem-dependent sample complexity guarantees. Finally, our experimental results demonstrate that HySRL surpasses the state-of-the-art pure online RL baseline.

Driven by inherent uncertainty and the sim-to-real gap, robust reinforcement learning (RL) seeks to improve resilience against the complexity and variability in agent-environment sequential interactions. Despite the existence of a large number of RL benchmarks, there is a lack of standardized benchmarks for robust RL. Current robust RL policies often focus on a specific type of uncertainty and are evaluated in distinct, one-off environments. In this work, we introduce Robust-Gymnasium, a unified modular benchmark designed for robust RL that supports a wide variety of disruptions across all key RL components—agents' observed state and reward, agents' actions, and the environment. Offering over sixty diverse task environments spanning control and robotics, safe RL, and multi-agent RL, it provides an open-source and user-friendly tool for the community to assess current methods and foster the development of robust RL algorithms. In addition, we benchmark existing standard and robust RL algorithms within this framework, uncovering significant deficiencies in each and offering new insights.

Monte Carlo Tree Search (MCTS) is a powerful framework for solving complex decision-making problems, yet it often relies on the assumption that the simulator and the real-world dynamics are identical. Although this assumption helps achieve the success of MCTS in games like Chess, Go, and Shogi, the real-world scenarios incur ambiguity due to their modeling mismatches in low-fidelity simulators. In this work, we present a new robust variant of MCTS that mitigates dynamical model ambiguities. Our algorithm addresses transition dynamics and reward distribution ambiguities to bridge the gap between simulation-based planning and real-world deployment. We incorporate a robust power mean backup operator and carefully designed exploration bonuses to ensure finite-sample convergence at every node in the search tree. We show that our algorithm achieves a convergence rate of $\mathcal{O}(n^{-1/2})$ for the value estimation at the root node, comparable to that of standard MCTS. Finally, we provide empirical evidence that our method achieves robust performance in planning problems even under significant ambiguity in the underlying reward distribution and transition dynamics.

Factored Markov Decision Processes (FMDPs) offer a promising framework for overcoming the curse of dimensionality in reinforcement learning (RL) by decomposing high-dimensional MDPs into smaller and independently evolving components. Despite their potential, existing studies on FMDPs face three key limitations: reliance on perfectly factorizable models, suboptimal sample complexity guarantees for model-based algorithms, and the absence of model-free algorithms. To address these challenges, we introduce approximate factorization, which extends FMDPs to handle imperfectly factored models. Moreover, we develop a model-based algorithm and a model-free algorithm (in the form of variance-reduced Q-learning), both achieving the first near-minimax sample complexity guarantees for FMDPs. A key novelty in the design of these two algorithms is the development of a graph-coloring-based optimal synchronous sampling strategy. Numerical simulations based on the wind farm storage control problem corroborate our theoretical findings.

Standard multi-agent reinforcement learning (MARL) algorithms are vulnerable to sim-to-real gaps. To address this, distributionally robust Markov games (RMGs) have been proposed to enhance robustness in MARL by optimizing the worst-case performance when game dynamics shift within a prescribed uncertainty set. RMGs remains under-explored, from reasonable problem formulation to the development of sample-efficient algorithms. Two notorious and open challenges are the formulation of the uncertainty set and whether the corresponding RMGs can overcome the curse of multiagency, where the sample complexity scales exponentially with the number of agents. In this work, we propose a natural class of RMGs inspired by behavioral economics, where each agent's uncertainty set is shaped by both the environment and the integrated behavior of other agents. We first establish the well-posedness of this class of RMGs by proving the existence of game-theoretic solutions such as robust Nash equilibria and coarse correlated equilibria (CCE). Assuming access to a generative model, we then introduce a sample-efficient algorithm for learning the CCE whose sample complexity scales polynomially with all relevant parameters. To the best of our knowledge, this is the first algorithm to break the curse of multiagency for RMGs, regardless of the uncertainty set formulation.

This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient algorithm may incur only the smaller among the reward and dueling-based regret for each individual arm. We propose two fusion approaches: (1) a simple elimination fusion algorithm that leverages both feedback types to explore all arms and unifies collected information by sharing a common candidate arm set, and (2) a decomposition fusion algorithm that selects the more effective feedback to explore the corresponding arms and randomly assigns one feedback type for exploration and the other for exploitation in each round. The elimination fusion experiences a suboptimal multiplicative term of the number of arms in regret due to the intrinsic suboptimality of dueling elimination. In contrast, the decomposition fusion achieves regret matching the lower bound up to a constant under a common assumption. Extensive experiments confirm the efficacy of our algorithms and theoretical results.

Deploying reinforcement learning (RL) safely in the real world is challenging, as policies trained in simulators must face the inevitable *sim-to-real gap*. Robust safe RL techniques are provably safe, however difficult to scale, while domain randomization is more practical yet prone to unsafe behaviors. We address this gap by proposing SPiDR, short for Sim-to-real via Pessimistic Domain Randomization—a scalable algorithm with provable guarantees for safe sim-to-real transfer. SPiDR uses domain randomization to incorporate the uncertainty about the sim-to-real gap into the safety constraints, making it versatile and highly compatible with existing training pipelines. Through extensive experiments on sim-to-sim benchmarks and two distinct real-world robotic platforms, we demonstrate that SPiDR effectively ensures safety despite the sim-to-real gap while maintaining strong performance.

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the cumulative reward while satisfying a constraint, even when there is a mismatch between the real model and an accessible simulator/nominal model. In particular, we consider the robust constrained Markov decision problem (RCMDP) where an agent needs to maximize the reward and satisfy the constraint against the worst possible stochastic model under the uncertainty set centered around an unknown nominal model. Primal-dual methods, effective for standard constrained MDP (CMDP), are not applicable here because of the lack of the strong duality property. Further, one cannot apply the standard robust value-iteration based approach on the composite value function, either, as the worst-case models may be different for the reward value function and the constraint value function. We propose a novel technique that effectively minimizes the constraint value function--to satisfy the constraints; on the other hand, when all the constraints are satisfied, it can simply maximize the robust reward value function. We prove that such an algorithm finds a policy with at most $\epsilon$ sub-optimality and a feasible policy after $O(\epsilon^{-2})$ iterations. In contrast to the state-of-the-art method, we do not need to employ a binary search; thus, we reduce the computation time and achieve a better performance, especially for continuous state-space.

Fairness and action smoothness are two crucial considerations in many online optimization problems, but they have yet to be addressed simultaneously. In this paper, we study a new and challenging setting of fairness-regularized smoothed online convex optimization with switching costs. First, to highlight the fundamental challenges introduced by the long-term fairness regularizer evaluated based on the entire sequence of actions, we prove that even without switching costs, no online algorithms can possibly achieve a sublinear regret or finite competitive ratio compared to the offline optimal algorithm as the problem episode length $T$ increases. Then, we propose **FairOBD** (Fairness-regularized Online Balanced Descent), which reconciles the tension between minimizing the hitting cost, switching cost, and fairness cost. Concretely, **FairOBD** decomposes the long-term fairness cost into a sequence of online costs by introducing an auxiliary variable and then leverages the auxiliary variable to regularize the online actions for fair outcomes. Based on a new approach to account for switching costs, we prove that **FairOBD** offers a worst-case asymptotic competitive ratio against a novel benchmark---the optimal offline algorithm with parameterized constraints---by considering $T\to\infty$. Finally, we run trace-driven experiments of dynamic computing resource provisioning for socially responsible AI inference to empirically evaluate **FairOBD**, showing that **FairOBD** can effectively reduce the total fairness-regularized cost and better promote fair outcomes compared to existing baseline solutions.

We study the value of stochastic predictions in online optimal control with random disturbances. Prior work provides performance guarantees based on prediction error but ignores the stochastic dependence between predictions and disturbances. We introduce a general framework modeling their joint distribution and define "prediction power" as the control cost improvement from the optimal use of predictions compared to ignoring the predictions. In the time-varying Linear Quadratic Regulator (LQR) setting, we derive a closed-form expression for prediction power and discuss its mismatch with prediction accuracy and connection with online policy optimization. To extend beyond LQR, we study general dynamics and costs. We establish a lower bound on prediction power under two sufficient conditions that generalize the properties of the LQR setting, characterizing the fundamental benefit of incorporating stochastic predictions. We apply this lower bound to non-quadratic costs and show that even weakly dependent predictions yield significant performance gains.

Traditional reinforcement learning (RL) assumes the agents make decisions based on Markov decision processes (MDPs) with one-step transition models. In many real-world applications, such as energy management and stock investment, agents can access multi-step predictions of future states, which provide additional advantages for decision making. However, multi-step predictions are inherently high-dimensional: naively embedding these predictions into an MDP leads to an exponential blow-up in state space and the curse of dimensionality. Moreover, existing RL theory provides few tools to analyze prediction-augmented MDPs, as it typically works on one-step transition kernels and cannot accommodate multi-step predictions with errors or partial action-coverage. We address these challenges with three key innovations: First, we propose the \emph{Bayesian value function} to characterize the optimal prediction-aware policy tractably. Second, we develop a novel \emph{Bellman–Jensen Gap} analysis on the Bayesian value function, which enables characterizing the value of imperfect predictions. Third, we introduce BOLA (Bayesian Offline Learning with Online Adaptation), a two-stage model-based RL algorithm that separates offline Bayesian value learning from lightweight online adaptation to real-time predictions. We prove that BOLA remains sample-efficient even under imperfect predictions. We validate our theory and algorithm on synthetic MDPs and a real-world wind energy storage control problem.

While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many real-world applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized Certainty-Equivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR). Furthermore, standard post-hoc CRC can degrade average-case performance due to its lack of feedback to the model. To address this, we introduce "conformal risk training," an end-to-end approach that differentiates through conformal OCE risk control _during model training or fine-tuning_. Our method achieves provable risk guarantees while demonstrating significantly improved average-case performance over post-hoc approaches on applications to controlling classifiers' false negative rate and controlling financial risk in battery storage operation.

As large-scale data processing workloads continue to grow, their carbon footprint raises concerns. Prior research on carbon-aware schedulers has focused on shifting computation to align with the availability of low-carbon energy, but these approaches assume that each task can be executed independently. In contrast, data processing jobs have precedence constraints that complicate decisions, since delaying an upstream "bottleneck" task to a low-carbon period also blocks downstream tasks, impacting makespan. In this paper, we show that carbon-aware scheduling for data processing benefits from knowledge of both time-varying carbon and precedence constraints. Our main contribution is PCAPS, a carbon-aware scheduler that builds on state-of-the-art scoring or probability-based techniques - in doing so, it explicitly relates the structural importance of each task against the time-varying characteristics of carbon intensity. To illustrate gains due to fine-grained task-level scheduling, we also study CAP, a wrapper for any carbon-agnostic scheduler that generalizes the provisioning ideas of PCAPS. Both techniques allow a user-configurable priority between carbon and makespan, and we give basic analytic results to relate the trade-off between these objectives. Our prototype on a 100-node Kubernetes cluster shows that a moderate configuration of PCAPS reduces carbon footprint by up to 32.9% without significantly impacting total efficiency.

We study the design of risk-sensitive online algorithms, in which risk measures are used in the competitive analysis of randomized online algorithms. We introduce the CVaR$_\delta$-competitive ratio ($\delta$-CR) using the conditional value-at-risk of an algorithm’s cost, which measures the expectation of the $(1-\delta)$-fraction of worst outcomes against the offline optimal cost, and use this measure to study three online optimization problems: continuous-time ski rental, discrete-time ski rental, and one-max search. The structure of the optimal $\delta$-CR and algorithm varies significantly between problems: we prove that the optimal $\delta$-CR for continuous-time ski rental is $2-2^{-\Theta(\frac{1}{1-\delta})}$, obtained by an algorithm described by a delay differential equation. In contrast, in discrete-time ski rental with buying cost $B$, there is an abrupt phase transition at $\delta = 1 - \Theta(\frac{1}{\log B})$, after which the classic deterministic strategy is optimal. Similarly, one-max search exhibits a phase transition at $\delta = \frac{1}{2}$, after which the classic deterministic strategy is optimal; we also obtain an algorithm that is asymptotically optimal as $\delta \todown 0$ that arises as the solution to a delay differential equation.

We study online policy optimization in nonlinear time-varying systems where the true dynamical models are unknown to the controller. This problem is challenging because, unlike in linear systems, the controller cannot obtain globally accurate estimations of the ground-truth dynamics using local exploration. We propose a meta-framework that combines a general online policy optimization algorithm (\texttt{ALG}) with a general online estimator of the dynamical system’s model parameters (\texttt{EST}). We show that if the hypothetical joint dynamics induced by \texttt{ALG} with \emph{known} parameters satisfies several desired properties, the joint dynamics under \emph{inexact} parameters from \texttt{EST} will be robust to errors. Importantly, the final regret only depends on \texttt{EST}’s predictions on the visited trajectory, which relaxes a bottleneck on identifying the true parameters globally. To demonstrate our framework, we develop a computationally efficient variant of Gradient-based Adaptive Policy Selection, called Memoryless GAPS (M-GAPS), and use it to instantiate \texttt{ALG}. Combining \mbox{M-GAPS} with online gradient descent to instantiate \texttt{EST} yields (to our knowledge) the first local regret bound for online policy optimization in nonlinear time-varying systems with unknown dynamics.

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

We study the smoothed online quadratic optimization (SOQO) problem where, at each round $t$, a player plays an action $x_t$ in response to a quadratic hitting cost and an additional squared $\ell_2$-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 $\Omega(T)$ 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 introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions $\mathbf{x}_t$ in a metric space $(X,d)$ to simultaneously minimize their hitting cost $f_t(\mathbf{x}_t)$ and switching cost as determined by the metric. Over the time horizon $T$, the player must satisfy a long-term demand constraint $\sum_t c(\mathbf{x}_t) \geq 1$, where $c(\mathbf{x}_t)$ denotes the fraction of demand satisfied at time $t$. Such problems can find a wide array of applications to online resource allocation in sustainable energy/computing systems. We devise optimal competitive and learning-augmented algorithms for the case of bounded hitting cost gradients and weighted $\ell_1$ metrics, and further show that our proposed algorithms perform well in numerical experiments.

This paper studies uncertainty set estimation for unknown linear systems. Uncertainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this paper focuses on set membership estimation (SME). Though good numerical performances have attracted applications of SME in the control literature, the non-asymptotic convergence rate of SME for linear systems remains an open question. This paper provides the first convergence rate bounds for SME and discusses variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME’s practical promise.

The robust $\phi$-regularized Markov Decision Process (RRMDP) framework focuses on designing control policies that are robust against parameter uncertainties due to mismatches between the simulator (nominal) model and real-world settings. This work makes two important contributions. First, we propose a model-free algorithm called Robust $\phi$-regularized fitted Q-iteration for learning an $\epsilon$-optimal robust policy that uses only the historical data collected by rolling out a behavior policy (with robust exploratory requirement) on the nominal model. To the best of our knowledge, we provide the first unified analysis for a class of $\phi$-divergences achieving robust optimal policies in high-dimensional systems of arbitrary large state space with general function approximation. Second, we introduce the hybrid robust $\phi$-regularized reinforcement learning framework to learn an optimal robust policy using both historical data and online sampling. Towards this framework, we propose a model-free algorithm called Hybrid robust Total-variation-regularized Q-iteration. To the best of our knowledge, we provide the first improved out-of-data-distribution assumption in large-scale problems of arbitrary large state space with general function approximation under the hybrid robust $\phi$-regularized reinforcement learning framework.

To overcome the sim-to-real gap in reinforcement learning (RL), learned policies must maintain robustness against environmental uncertainties. While robust RL has been widely studied in single-agent regimes, in multi-agent environments, the problem remains understudied—despite the fact that the problems posed by environmental uncertainties are often exacerbated by strategic interactions. This work focuses on learning in distributionally robust Markov games (RMGs), a robust variant of standard Markov games, wherein each agent aims to learn a policy that maximizes its own worst-case performance when the deployed environment deviates within its own prescribed uncertainty set. This results in a set of robust equilibrium strategies for all agents that align with classic notions of game-theoretic equilibria. Assuming a non-adaptive sampling mechanism from a generative model, we propose a sample-efficient model-based algorithm (DRNVI) with finite-sample complexity guarantees for learning robust variants of various notions of game-theoretic equilibria. We also establish an information-theoretic lower bound for solving RMGs, which confirms the near-optimal sample complexity of DRNVI with respect to problem-dependent factors such as the size of the state space, the target accuracy, and the horizon length.

Online Budgeted Matching (OBM) is a classic problem with important applications in online advertising, online service matching, revenue management, and beyond. Traditional online algorithms typically assume a small bid setting, where the maximum bid-to-budget ratio ($\kappa$) is infinitesimally small. While recent algorithms have tried to address scenarios with non-small or general bids, they often rely on the Fractional Last Matching (FLM) assumption, which allows for accepting partial bids when the remaining budget is insufficient. This assumption, however, does not hold for many applications with indivisible bids. In this paper, we remove the FLM assumption and tackle the open problem of OBM with general bids. We first establish an upper bound of $1-\kappa$ on the competitive ratio for any deterministic online algorithm. We then propose a novel meta algorithm, called MetaAd, which reduces to different algorithms with first known provable competitive ratios parameterized by the maximum bid-to-budget ratio $\kappa\in [0,1]$. As a by-product, we extend MetaAd to the FLM setting and get provable competitive algorithms. Finally, we apply our competitive analysis to the design learning- augmented algorithms.

To address the challenges of sim-to-real gap and sample efficiency in reinforcement learning (RL), this work studies distributionally robust Markov decision processes (RMDPs) --- optimize the worst-case performance when the deployed environment is within an uncertainty set around some nominal MDP. Despite recent efforts, the sample complexity of RMDPs has remained largely undetermined. While the statistical implications of distributional robustness in RL have been explored in some specific cases, the generalizability of the existing findings remains unclear, especially in comparison to standard RL. Assuming access to a generative model that samples from the nominal MDP, we examine the sample complexity of RMDPs using a class of generalized $L_p$ norms as the 'distance' function for the uncertainty set, under two commonly adopted $sa$-rectangular and $s$-rectangular conditions. Our results imply that RMDPs can be more sample-efficient to solve than standard MDPs using generalized $L_p$ norms in both $sa$- and $s$-rectangular cases, potentially inspiring more empirical research. We provide a near-optimal upper bound and a matching minimax lower bound for the $sa$-rectangular scenarios. For $s$-rectangular cases, we improve the state-of-the-art upper bound and also derive a lower bound using $L_\infty$ norm that verifies the tightness.

Safe reinforcement learning (RL) is crucial for deploying RL agents in real-world applications, as it aims to maximize long-term rewards while satisfying safety constraints. However, safe RL often suffers from sample inefficiency, requiring extensive interactions with the environment to learn a safe policy. We propose Efficient Safe Policy Optimization (ESPO), a novel approach that enhances the efficiency of safe RL through sample manipulation. ESPO employs an optimization framework with three modes: maximizing rewards, minimizing costs, and balancing the trade-off between the two. By dynamically adjusting the sampling process based on the observed conflict between reward and safety gradients, ESPO theoretically guarantees convergence, optimization stability, and improved sample complexity bounds. Experiments on the Safety-MuJoCo and Omnisafe benchmarks demonstrate that ESPO significantly outperforms existing primal-based and primal-dual-based baselines in terms of reward maximization and constraint satisfaction. Moreover, ESPO achieves substantial gains in sample efficiency, requiring 25--29\% fewer samples than baselines, and reduces training time by 21--38\%.

The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for the other agents. The idea is to plan an agent's own actions with respect to those types which it believes are most likely to maximize the payoff. However, the type beliefs are often learned from past actions and likely to be incorrect. With this perspective in mind, we consider an agent in a game with type predictions of other components, and investigate the impact of incorrect beliefs to the agent’s payoff. In particular, we formally define a tradeoff between risk and opportunity by comparing the payoff obtained against the optimal payoff, which is represented by a gap caused by trusting or distrusting the learned beliefs.Our main results characterize the tradeoff by establishing upper and lower bounds on the Pareto front for both normal-form and stochastic Bayesian games, with numerical results provided.

The primary objective of adaptive bitrate (ABR) streaming is to enhance users' quality of experience (QoE) by dynamically adjusting the video bitrate in response to changing network conditions. However, users often find frequent bitrate switching frustrating due to the resulting inconsistency in visual quality over time, especially during live streaming when buffer lengths are short. In this paper, we propose a practical smoothness optimized dynamic adaptive (SODA) controller that specifically addresses this problem while remaining deployable. SODA is backed by theoretical guarantees and has shown superior performance in empirical evaluations. Specifically, our numerical simulations show a 9.55% to 27.8% QoE improvement and our prototype evaluation shows a 30.4% QoE improvement compared to the state-of-the-art baselines. In order to be widely deployable, SODA performs bitrate horizon planning in polynomial time compared to brute force approaches that suffer from exponential complexity. To demonstrate its real-world practicality, we deployed SODA on a wide range of devices within the production network of Amazon Prime Video. Production experiments show that SODA reduced bitrate switching by up to 88.8% and increased average stream viewing duration by up to 5.91% compared to a fine-tuned production baseline.

We consider two-player zero-sum stochastic games and propose a two-timescale variant of Q-learning with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale Q-learning, the fast-timescale iterates are updated in spirit to the stochastic gradient descent for minimizing a Bellman error variant and the slow-timescale iterates (which we use to compute the policies) are updated by taking a convex combination between its previous iterate and the latest fast-timescale iterate. In the special case of linear function approximation, we present, to the best of our knowledge, the first last-iterate finite-sample bound for payoff-based independent learning dynamics of these types.

We examine the problem of designing learning-augmented algorithms for metrical task systems (MTS) that exploit machine-learned advice while maintaining rigorous, worst-case guarantees on performance. We propose an algorithm, DART, that achieves this dual objective, providing cost within a multiplicative factor $(1+\epsilon)$ of the machine-learned advice (i.e., consistency) while ensuring cost within a multiplicative factor $2^{O(1/\epsilon)}$ of a baseline robust algorithm (i.e., robustness) for any $\epsilon > 0$. We show that this exponential tradeoff between consistency and robustness is unavoidable in general, but that in important subclasses of MTS, such as when the metric space has bounded diameter and in the $k$-server problem, our algorithm achieves improved, polynomial tradeoffs between consistency and robustness.

We study contextual combinatorial bandits with probabilistically triggered arms (C$^2$MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C$^2$-UCB-T algorithm and propose a novel analysis that achieves an $\tilde{O}(d\sqrt{KT})$ regret bound, removing a potentially exponentially large factor $O(1/p_{\min})$, where $d$ is the dimension of contexts, $p_{\min}$ is the minimum positive probability that any arm can be triggered, and batch-size $K$ is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC$^2$-UCB and derive a regret bound $\tilde{O}(d\sqrt{T})$, which is independent of the batch-size $K$. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C$^2$MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

In this work, we study two-player zero-sum stochastic games and develop a variant of the smoothed best-response learning dynamics that combines independent learning dynamics for matrix games with the minimax value iteration for stochastic games. The resulting learning dynamics are payoff-based, convergent, rational, and symmetric between the two players. Our theoretical results present to the best of our knowledge the first last-iterate finite-sample analysis of such independent learning dynamics. To establish the results, we develop a coupled Lyapunov drift approach to capture the evolution of multiple sets of coupled and stochastic iterates, which might be of independent interest.

We study the tradeoff between consistency and robustness in the context of a single-trajectory time-varying Markov Decision Process (MDP) with untrusted machine-learned advice. Our work departs from the typical approach of treating advice as coming from black-box sources by instead considering a setting where additional information about how the advice is generated is available. We prove a first-of-its-kind consistency and robustness tradeoff given Q-value advice under a general MDP model that includes both continuous and discrete state/action spaces. Our results highlight that utilizing Q-value advice enables dynamic pursuit of the better of machine-learned advice and a robust baseline, thus result in near-optimal performance guarantees, which provably improves what can be obtained solely with black-box advice.

We study a general form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically, we prove that RCL is able to guarantee $(1+\lambda)$-competitiveness against any given expert for any $\lambda>0$, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly, RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay. We demonstrate the improvement of RCL in both robustness and average performance using battery management as a case study.

We study online adaptive policy selection in systems with time-varying costs and dynamics. We develop the Gradient-based Adaptive Policy Selection (GAPS) algorithm together with a general analytical framework for online policy selection via online optimization. Under our proposed notion of contractive policy classes, we show that GAPS approximates the behavior of an ideal online gradient descent algorithm on the policy parameters while requiring less information and computation. When convexity holds, our algorithm is the first to achieve optimal policy regret. When convexity does not hold, we provide the first local regret bound for online policy selection. Our numerical experiments show that GAPS can adapt to changing environments more quickly than existing benchmarks.

This paper studies the problem of Anytime-Competitive Markov Decision Process (A-CMDP). Existing works on Constrained Markov Decision Processes (CMDPs) aim to optimize the expected reward while constraining the expected cost over random dynamics, but the cost in a specific episode can still be unsatisfactorily high. In contrast, the goal of A-CMDP is to optimize the expected reward while guaranteeing a bounded cost in each round of any episode against a policy prior. We propose a new algorithm, called Anytime-Competitive Reinforcement Learning (ACRL), which provably guarantees the anytime cost constraints. The regret analysis shows the policy asymptotically matches the optimal reward achievable under the anytime competitive constraints. Experiments on the application of carbon-intelligent computing verify the reward performance and cost constraint guarantee of ACRL.

The lack of standardized benchmarks for reinforcement learning (RL) in sustainability applications has made it difficult to both track progress on specific domains and identify bottlenecks for researchers to focus their efforts. In this paper, we present SustainGym, a suite of five environments designed to test the performance of RL algorithms on realistic sustainable energy system tasks, ranging from electric vehicle charging to carbon-aware data center job scheduling. The environments test RL algorithms under realistic distribution shifts as well as in multi-agent settings. We show that standard off-the-shelf RL algorithms leave significant room for improving performance and highlight the challenges ahead for introducing RL to real-world sustainability tasks.

Online learning to rank (OLTR) is a sequential decision-making problem where a learning agent selects an ordered list of items and receives feedback through user clicks. Although potential attacks against OLTR algorithms may cause serious losses in real-world applications, there is limited knowledge about adversarial attacks on OLTR. This paper studies attack strategies against multiple variants of OLTR. Our first result provides an attack strategy against the UCB algorithm on classical stochastic bandits with binary feedback, which solves the key issues caused by bounded and discrete feedback that previous works cannot handle. Building on this result, we design attack algorithms against UCB-based OLTR algorithms in position-based and cascade models. Finally, we propose a general attack strategy against any algorithm under the general click model. Each attack algorithm manipulates the learning agent into choosing the target attack item $T-o(T)$ times, incurring a cumulative cost of $o(T)$. Experiments on synthetic and real data further validate the effectiveness of our proposed attack algorithms.

We introduce a class of networked Markov potential games where agents are associated with nodes in a network. Each agent has its own local potential function, and the reward of each agent depends only on the states and actions of agents within a neighborhood. In this context, we propose a localized actor-critic algorithm. The algorithm is scalable since each agent uses only local information and does not need access to the global state. Further, the algorithm overcomes the curse of dimensionality through the use of function approximation. Our main results provide finite-sample guarantees up to a localization error and a function approximation error. Specifically, we achieve an $\tilde{\mathcal{O}}(\tilde{\epsilon}^{-4})$ sample complexity measured by the averaged Nash regret. This is the first finite-sample bound for multi-agent competitive games that does not depend on the number of agents.

We consider the problem of convex function chasing with black-box advice, where an online decision-maker aims to minimize the total cost of making and switching between decisions in a normed vector space, aided by black-box advice such as the decisions of a machine-learned algorithm. The decision-maker seeks cost comparable to the advice when it performs well, known as \emph{consistency}, while also ensuring worst-case \emph{robustness} even when the advice is adversarial. We first consider the common paradigm of algorithms that switch between the decisions of the advice and a competitive algorithm, showing that no algorithm in this class can improve upon 3-consistency while staying robust. We then propose two novel algorithms that bypass this limitation by exploiting the problem’s convexity. The first, $\textsc{Interp}$, achieves $(\sqrt{2}+\epsilon)$-consistency and $\mathcal{O}(\frac{C}{\epsilon^2})$-robustness for any $\epsilon > 0$, where $C$ is the competitive ratio of an algorithm for convex function chasing or a subclass thereof. The second, $\textsc{BdInterp}$, achieves $(1+\epsilon)$-consistency and $\mathcal{O}(\frac{CD}{\epsilon})$-robustness when the problem has bounded diameter $D$. Further, we show that $\textsc{BdInterp}$ achieves near-optimal consistency-robustness trade-off for the special case where cost functions are $\alpha$-polyhedral.

We study the problem of networked online convex optimization, where each agent individually decides on an action at every time step and agents cooperatively seek to minimize the total global cost over a finite horizon. The global cost is made up of three types of local costs: convex node costs, temporal interaction costs, and spatial interaction costs. In deciding their individual action at each time, an agent has access to predictions of local cost functions for the next $k$ time steps in an $r$-hop neighborhood. Our work proposes a novel online algorithm, Localized Predictive Control (LPC), which generalizes predictive control to multi-agent systems. We show that LPC achieves a competitive ratio of $1 + \tilde{O}(\rho_T^k) + \tilde{O}(\rho_S^r)$ in an adversarial setting, where $\rho_T$ and $\rho_S$ are constants in $(0, 1)$ that increase with the relative strength of temporal and spatial interaction costs, respectively. This is the first competitive ratio bound on decentralized predictive control for networked online convex optimization. Further, we show that the dependence on $k$ and $r$ in our results is near optimal by lower bounding the competitive ratio of any decentralized online algorithm.

Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current state-of-the-art approaches require a sample complexity linear in $n$, the state dimension, which incurs a state norm that blows up exponentially in $n$. We propose a novel algorithm based on spectral decomposition that only needs to learn ``a small part'' of the dynamical matrix acting on its unstable subspace. We show that, under proper assumptions, our algorithm stabilizes an LTI system on a single trajectory with $O(k \log n)$ samples, where $k$ is the instability index of the system. This represents the first sub-linear sample complexity result for the stabilization of LTI systems under the regime when $k = o(n)$.

We study Model Predictive Control (MPC) and propose a general analysis pipeline to bound its dynamic regret. The pipeline first requires deriving a perturbation bound for a finite-time optimal control problem. Then, the perturbation bound is used to bound the per-step error of MPC, which leads to a bound on the dynamic regret. Thus, our pipeline reduces the study of MPC to the well-studied problem of perturbation analysis, enabling the derivation of regret bounds of MPC under a variety of settings. To demonstrate the power of our pipeline, we use it to generalize existing regret bounds on MPC in linear time-varying (LTV) systems to incorporate prediction errors on costs, dynamics, and disturbances. Further, our pipeline leads to regret bounds on MPC in systems with nonlinear dynamics and constraints.

The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on non-worst-case inputs. In this paper, we develop an approach for data-driven design of online algorithms that maintain near-optimal worst-case guarantees while also performing learning in order to perform well for typical inputs. Our approach is to identify policy classes that admit global worst-case guarantees, and then perform learning using historical data within the policy classes. We demonstrate the approach in the context of two classical problems, online knapsack and online set cover, proving competitive bounds for rich policy classes in each case. Additionally, we illustrate the practical implications via a case study on electric vehicle charging.

Cloud platforms' growing energy demand and carbon emissions are raising concern about their environmental sustainability. The current approach to enabling sustainable clouds focuses on improving energy-efficiency and purchasing carbon offsets. These approaches have limits: many cloud data centers already operate near peak efficiency, and carbon offsets cannot scale to near zero carbon where there is little carbon left to offset. Instead, enabling sustainable clouds will require applications to adapt to when and where unreliable low-carbon energy is available. Applications cannot do this today because their energy use and carbon emissions are not visible to them, as the energy system provides the rigid abstraction of a continuous, reliable energy supply. This vision paper instead advocates for a "carbon first" approach to cloud design that elevates carbon-efficiency to a firs--class metric. To do so, we argue that cloud platforms should virtualize the energy system by exposing visibility into, and software-defined control of, it to applications, enabling them to define their own abstractions for managing energy and carbon emissions based on their own requirements.

We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future $k$ time steps. We show that when the prediction window $k$ is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of $O(\lambda^k T)$, where $\lambda < 1$ is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. We also show a variation of predictive control obtains the first competitive bound for the control of linear time-varying systems: $1 + O(\lambda^k)$. Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.

We study multi-agent reinforcement learning (MARL) in a stochastic network of agents. The objective is to find localized policies that maximize the (discounted) global reward. In general, scalability is a challenge in this setting because the size of the global state/action space can be exponential in the number of agents. Scalable algorithms are only known in cases where dependencies are static, fixed and local, e.g., between neighbors in a fixed, time-invariant underlying graph. In this work, we propose a Scalable Actor Critic framework that applies in settings where the dependencies can be non-local and stochastic, and provide a finite-time error bound that shows how the convergence rate depends on the speed of information spread in the network. Additionally, as a byproduct of our analysis, we obtain novel finite-time convergence results for a general stochastic approximation scheme and for temporal difference learning with state aggregation, which apply beyond the setting of MARL in networked systems.

This paper leverages machine-learned predictions to design competitive algorithms for online conversion problems with the goal of improving the competitive ratio when predictions are accurate (i.e., consistency), while also guaranteeing a worst-case competitive ratio regardless of the prediction quality (i.e., robustness). We unify the algorithmic design of both integral and fractional conversion problems, which are also known as the 1-max-search and one-way trading problems, into a class of online threshold-based algorithms (OTA). By incorporating predictions into design of OTA, we achieve the Pareto-optimal trade-off of consistency and robustness, i.e., no online algorithm can achieve a better consistency guarantee given for a robustness guarantee. We demonstrate the performance of OTA using numerical experiments on Bitcoin conversion.

While users claim to be concerned about privacy, often they do little to protect their privacy in their online actions. One prominent explanation for this "privacy paradox'' is that when an individual shares her data, it is not just her privacy that is compromised; the privacy of other individuals with correlated data is also compromised. This information leakage encourages oversharing of data and significantly impacts the incentives of individuals in online platforms. In this paper, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We design an incentive compatible mechanism that optimizes the worst-case trade-off between bias and variance of the estimation subject to a budget constraint, where the worst-case is over the unknown correlation between costs and data. Additionally, we characterize the structure of the optimal mechanism in closed form and study monotonicity and non-monotonicity properties of the marketplace.

We consider a general asynchronous Stochastic Approximation (SA) scheme featuring a weighted infinity-norm contractive operator, and prove a bound on its finite-time convergence rate on a single trajectory. Additionally, we specialize the result to asynchronous $Q$-learning. The resulting bound matches the sharpest available bound for synchronous $Q$-learning, and improves over previous known bounds for asynchronous $Q$-learning.

It has long been recognized that multi-agent reinforcement learning (MARL) faces significant scalability issues due to the fact that the size of the state and action spaces are exponentially large in the number of agents. In this paper, we identify a rich class of networked MARL problems where the model exhibits a local dependence structure that allows it to be solved in a scalable manner. Specifically, we propose a Scalable Actor-Critic (SAC) method that can learn a near optimal localized policy for optimizing the average reward with complexity scaling with the state-action space size of local neighborhoods, as opposed to the entire network. Our result centers around identifying and exploiting an exponential decay property that ensures the effect of agents on each other decays exponentially fast in their graph distance.

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.

We study the impact of predictions in online Linear Quadratic Regulator control with both stochastic and adversarial disturbances in the dynamics. In both settings, we characterize the optimal policy and derive tight bounds on the minimum cost and dynamic regret. Perhaps surprisingly, our analysis shows that the conventional greedy MPC approach is a near-optimal policy in both stochastic and adversarial settings. Specifically, for length-$T$ problems, MPC requires only $O(\log T)$ predictions to reach $O(1)$ dynamic regret, which matches (up to lower-order terms) our lower bound on the required prediction horizon for constant regret.

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio $3 + O(1/m)$, irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is $\epsilon$-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive algorithms for a variety of online problems across learning and control, including online variants of ridge regression, logistic regression, maximum likelihood estimation, and LQR control.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm. This lower bound shows that no algorithm can achieve a competitive ratio that is $o(m^{-1/2})$ as $m$ tends to zero. No existing algorithms have competitive ratios matching this bound, and we show that the state-of-the-art algorithm, Online Balanced Decent (OBD), has a competitive ratio that is $\Omega(m^{-2/3})$. We additionally propose two new algorithms, Greedy OBD (G-OBD) and Regularized OBD (R-OBD) and prove that both algorithms have an $O(m^{-1/2})$ competitive ratio. The result for G-OBD holds when the hitting costs are quasiconvex and the movement costs are the squared $\ell_2$ norm, while the result for R-OBD holds when the hitting costs are $m$-strongly convex and the movement costs are Bregman Divergences. Further, we show that R-OBD simultaneously achieves constant, dimension-free competitive ratio and sublinear regret when hitting costs are strongly convex.

We study \emph{smoothed online convex optimization}, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $\Omega(\sqrt{d})$ lower bound on the competitive ratio of any online algorithm, where $d$ is the dimension of the action space, we ask under what conditions this bound can be beaten. We introduce a novel algorithmic framework for this problem, Online Balanced Descent (OBD), which works by iteratively projecting the previous point onto a carefully chosen level set of the current cost function so as to balance the switching costs and hitting costs. We demonstrate the generality of the OBD framework by showing how, with different choices of “balance,” OBD can improve upon state-of-the-art performance guarantees for both competitive ratio and regret; in particular, OBD is the first algorithm to achieve a dimension-free competitive ratio, $3 + O(1/\alpha)$, for locally polyhedral costs, where $\alpha$ measures the “steepness” of the costs. We also prove bounds on the dynamic regret of OBD when the balance is performed in the dual space that are dimension-free and imply that OBD has sublinear static regret.

Despite the common practice of oversubscription, power capacity is largely under-utilized in data centers. A significant factor driving this under-utilization is fluctuation of the aggregate power demand, resulting in unused “spot (power) capacity”. In this paper, we tap into spot capacity for improving power infrastructure utilization in multi-tenant data centers, an important but under-explored type of data center where multiple tenants house their own physical servers. We propose a novel market, called SpotDC, to allocate spot capacity to tenants on demand. Specifically, SpotDC extracts tenants' racklevel spot capacity demand through an elastic demand function, based on which the operator sets the market price for spot capacity allocation. We evaluate SpotDC using both testbed experiments and simulations, demonstrating that SpotDC improves power infrastructure utilization and creates a “win-win” situation: the data center operator increases its profit (by nearly 10%), while tenants improve their performance (by 1.2-1.8x on average compared to the no spot capacity case, yet at a marginal cost).

Loyalty programs are important tools for sharing platforms seeking to grow supply. Online sharing platforms use loyalty programs to heavily subsidize resource providers, encouraging participation and boosting supply. As the sharing economy has evolved and competition has increased, the design of loyalty programs has begun to play a crucial role in the pursuit of maximal revenue. In this paper, we first characterize the optimal loyalty program for a platform with homogeneous users. We then show that optimal revenue in a heterogeneous market can be achieved by a class of multi-threshold loyalty program (MTLP) which admits a simple implementation-friendly structure. We also study the performance of loyalty programs in a setting with two competing sharing platforms, showing that the degree of heterogeneity is a crucial factor for both loyalty programs and pricing strategies. Our results show that sophisticated loyalty programs that reward suppliers via stepwise linear functions outperform simple sign-up bonuses, which give them a one time reward for participating.

The power capacity of multi-tenant data centers is typically oversubscribed in order to increase the utilization of expensive power infrastructure. This practice can create dangerous situations and compromise data center availability if the designed power capacity is exceeded. This paper demonstrates that current safeguards are vulnerable to well-timed power attacks launched by malicious tenants (i.e., attackers). Further, we demonstrate that there is a physical side channel --- a thermal side channel due to hot air recirculation --- that contains information about the benign tenants' runtime power usage and can enable a malicious tenant to time power attacks effectively. In particular, we design a state-augmented Kalman filter to extract this information from the side channel and guide an attacker to use its maximum power at moments that coincide with the benign tenants' high power demand, thus overloading the shared power capacity. Our experimental results show that an attacker can capture 54% of all attack opportunities, significantly compromising the data center availability. Finally, we discuss a set of possible defense strategies to safeguard the data center infrastructure against power attacks.

This paper studies how the efficiency of an online platform is impacted by the degree to which access of platform participants is open or controlled. The study is motivated by an emerging trend within platforms to impose increasingly fine-grained control over the options available to platform participants. While early online platforms allowed open access, e.g., Ebay allows any seller to interact with any buyer; modern platforms often impose matches directly, e.g., Uber directly matches drivers to riders. This control is performed with the goal of achieving more efficient market outcomes. However, the results in this paper highlight that imposing matches may create new strategic incentives that lead to increased inefficiency. In particular, in the context of networked Cournot competition, we prove that open access platforms guarantee social welfare within 7/16 of the optimal; whereas controlled allocation platforms can have social welfare unboundedly worse than optimal.

The growth of the sharing economy is driven by the emergence of sharing platforms, e.g., Uber and Lyft, that match owners looking to share their resources with customers looking to rent them. The design of such platforms is a complex mixture of economics and engineering, and how to "optimally" design such platforms is still an open problem. In this paper, we focus on the design of prices and subsidies in sharing platforms. Our results provide insights into the tradeoff between revenue maximizing prices and social welfare maximizing prices. Specifically, we introduce a novel model of sharing platforms and characterize the profit and social welfare maximizing prices in this model. Further, we bound the efficiency loss under profit maximizing prices, showing that there is a strong alignment between profit and efficiency in practical settings. Our results highlight that the revenue of platforms may be limited in practice due to supply short- ages; thus platforms have a strong incentive to encourage sharing via subsidies. We provide an analytic characterization of when such subsidies are valuable and show how to optimize the size of the subsidy provided. Finally, we validate the insights from our analysis using data from Didi Chuxing, the largest ridesharing platform in China.

Power oversubscription in data centers may occasionally trigger an emergency when the aggregate power demand exceeds the capacity. Handling such an emergency requires a graceful power capping solution that minimizes the performance loss. In this paper, we study power capping in a multi-tenant data center where the operator supplies power to multiple tenants that manage their own servers. Unlike owner-operated data centers, the operator lacks control over tenants' servers. To address this challenge, we propose a novel market mechanism based on supply function bidding, called COOP, to financially incentivize and coordinate tenants' power reduction for minimizing total performance loss (quantified in performance cost) while satisfying multiple power capping constraints. We build a prototype to show that COOP is efficient in terms of minimizing the total performance cost, even compared to the ideal but infeasible case that assumes the operator has full control over tenants' servers. We also demonstrate that COOP is "win-win", increasing the operator's profit (through oversubscription) and reducing tenants' cost (through financial compensation for their power reduction during emergencies).

We consider online convex optimization (OCO) problems with switching costs and noisy predictions. While the design of online algorithms for OCO problems has received considerable attention, the design of algorithms in the context of noisy predictions is largely open. To this point, two promising algorithms have been proposed: Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). The comparison of these policies is largely open. AFHC has been shown to provide better worst-case performance, while RHC outperforms AFHC in many realistic settings. In this paper, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both RHC and AFHC. We provide average-case analysis and concentration results for CHC policies, yielding the first analysis of RHC for OCO problems with noisy predictions. Further, we provide explicit results characterizing the optimal CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Our results provide a characterization of when AFHC outperforms RHC and vice versa, as well as when other CHC policies outperform both RHC and AFHC.

This paper studies design challenges faced by a geo-distributed cloud data market: which data to purchase (data purchasing) and where to place/replicate the data (data placement). We show that the joint problem of data purchasing and data placement within a cloud data market is NP-hard in general. However, we give a provably optimal algorithm for the case of a data market made up of a single data center, and then generalize the structure from the single data center setting and propose Datum, a near-optimal, polynomial-time algorithm for a geo-distributed data market.

This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response-time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we consider a setting where a bursty flow, modeled using heavy-tailed statistics, competes with a more benign, light-tailed flow. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee light-tailed delays for the light-tailed flow, without affecting the response-time tail for the heavy-tailed flow.

As clusters continue to grow in size and complexity, providing scalable and predictable performance is an increasingly important challenge. A crucial roadblock to achieving predictable performance is stragglers, i.e., tasks that take significantly longer than expected to run. At this point, speculative execution has been widely adopted to mitigate the impact of stragglers. However, speculation mechanisms are designed and operated independently of job scheduling when, in fact, scheduling a speculative copy of a task has a direct impact on the resources available for other jobs. In this work, we present Hopper, a job scheduler that is speculation-aware, i.e., that integrates the tradeoffs associated with speculation into job scheduling decisions. We implement both centralized and decentralized prototypes of the Hopper scheduler and show that 50% (66%) improvements over state-of-the-art centralized (decentralized) schedulers and speculation strategies can be achieved through the coordination of scheduling and speculation.

Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean.

Energy expenditure has become a significant fraction of data center operating costs. Recently, “geographical load balancing” has been proposed to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energy use. We explore whether the geographical diversity of Internet-scale systems can also provide environmental gains. Specifically, we explore whether geographical load balancing can encourage use of “green” renewable energy and reduce use of “brown” fossil fuel energy. We make two contributions. First, we derive three distributed algorithms for achieving optimal geographical load balancing. Second, we show that if the price of electricity is proportional to the instantaneous fraction of the total energy that is brown, then geographical load balancing significantly reduces brown energy use. However, the benefits depend strongly on dynamic energy pricing and the form of pricing used.

This paper initiates the study of the testable implications of choice data in settings where agents have privacy preferences. We adapt the standard conceptualization of consumer choice theory to a situation where the consumer is aware of, and has preferences over, the information revealed by her choices. The main message of the paper is that little can be inferred about consumers' preferences once we introduce the possibility that the consumer has concerns about privacy. This holds even when consumers' privacy preferences are assumed to be monotonic and separable. This motivates the consideration of stronger assumptions and, to that end, we introduce an additive model for privacy preferences that does have testable implications.

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by these policies. This observation has consequences when modeling service system performance, and our objective in this paper is to investigate those consequences.

Demand response is crucial for the incorporation of renewable energy into the grid. In this paper, we focus on a particularly promising industry for demand response: data centers. We use simulations to show that, not only are data centers large loads, but they can provide as much (or possibly more) flexibility as large-scale storage if given the proper incentives. However, due to the market power most data centers maintain, it is difficult to design programs that are efficient for data center demand response. To that end, we propose that prediction-based pricing is an appealing market design, and show that it outperforms more traditional supply function bidding mechanisms in situations where market power is an issue. However, prediction-based pricing may be inefficient when predictions are inaccurate, and so we provide analytic, worst-case bounds on the impact of prediction error on the efficiency of prediction-based pricing. These bounds hold even when network constraints are considered, and highlight that prediction-based pricing is surprisingly robust to prediction error.

The increasing penetration of intermittent, unpredictable renewable energy sources such as wind energy, poses significant challenges for utility companies trying to incorporate renewable energy in their portfolio. In this work, we study the problem of conventional energy procurement in the presence of intermittent renewable resources. We model the problem as a variant of the newsvendor problem, in which the presence of renewable resources induces supply side uncertainty, and in which conventional energy may be procured in three stages to balance supply and demand. We compute closed-form expressions for the optimal energy procurement strategy and study the impact of increasing renewable penetration, and of proposed changes to the structure of electricity markets. We explicitly characterize the impact of a growing renewable penetration on the procurement policy by considering a scaling regime that models the aggregation of unpredictable renewable sources. A key insight from our results is that there is a separation between the impact of the stochastic nature of this aggregation, and the impact of market structure and forecast accuracy. Additionally, we study the impact on procurement of two proposed changes to the market structure: the addition and the placement of an intermediate market. We show that addition of an intermediate market does not necessarily increase the efficiency of utilization of renewable sources. Further, we show that the optimal placement of the intermediate market is insensitive to the level of renewable penetration.

Today’s communication networks and networked systems are highly complex and heterogeneous \nand are often owned by profit-making entities. For new technologies or \ninfrastructure designs to be adopted, they must not only be based on sound engineering \nperformance considerations but also present the right economic incentives. Recent \nchanges in regulations of the telecommunication industry make such economic considerations \neven more urgent. For instance, new concerns such as network neutrality \nhave a significant impact on the evolution of communication networks. \nAt the same time, communication networks and networked systems support increasing \neconomic activity based on applications and services such as cloud computing, \nsocial networks, and peer-to-peer networks. These applications pose new challenges \nincluding the development of good pricing and incentive mechanisms to promote effective \nsystem-wide behavior. Similarly, the security and privacy of these applications are \nthemselves heavily dependent on economic considerations, which therefore need to be \nfully understood. \nTo address these questions, this special issue brings together a relevant set of state-of-the-art research contributions on complementary topics including communication \nnetworks, wireless networks, web content and security, and the use of multidisciplinary \napproaches ranging from game theory and economic modeling to algorithms \nand mechanism design, and including empirical studies.

We consider algorithms for “smoothed online convex optimization” problems, a variant of the class of online convex optimization problems that is strongly related to metrical task systems. Prior literature on these problems has focused on two performance metrics: regret and the competitive ratio. There exist known algorithms with sublinear regret and known algorithms with constant competitive ratios; however, no known algorithm achieves both simultaneously. We show that this is due to a fundamental incompatibility between these two metrics - no algorithm (deterministic or randomized) can achieve sublinear regret and a constant competitive ratio, even in the case when the objective functions are linear. However, we also exhibit an algorithm that, for the important special case of one dimensional decision spaces, provides sublinear regret while maintaining a competitive ratio that grows arbitrarily slowly.

This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we study an extreme setting with two traffic flows, one heavy-tailed, and one light-tailed. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee light-tailed delays for the light-tailed flow, without affecting the response time tail for the heavy-tailed flow.

Energy consumption imposes a significant cost for data centers; yet much of that energy is used to maintain excess service capacity during periods of predictably low load. Resultantly, there has recently been interest in developing designs that allow the service capacity to be dynamically resized to match the current workload. However, there is still much debate about the value of such approaches in real settings. In this paper, we show that the value of dynamic resizing is highly dependent on statistics of the workload process. In particular, both slow time-scale non-stationarities of the workload (e.g., the peak-to-mean ratio) and the fast time-scale stochasticity (e.g., the burstiness of arrivals) play key roles. To illustrate the impact of these factors, we combine optimization-based modeling of the slow time-scale with stochastic modeling of the fast time scale.

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant payoff functions. We prove that high complexity (high rank) has empirical consequences when arbitrary data is considered. Additionally, we prove that, in more restrictive classes of data (termed laminar), any observation is rationalizable using a low-rank game: specifically a zero-sum game. Hence complexity as a structural property of a game is not always testable. Finally, we prove a general result connecting the structure of the feasible data sets with the highest rank that may be needed to rationalize a set of observations.

We consider the problem of designing distribution rules to share `welfare' (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games, which includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions $W$, we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some `ground' welfare functions $W$, which can be distinct from W. However, if budget-balance is required in addition to the existence of a Nash equilibrium, then $W$ must be the same as $W$. We also provide an alternate characterization of this space in terms of `generalized' marginal contributions, which is more appealing from the point of view of computational tractability. A possibly surprising consequence of our result is that, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is \textitnecessary to work within the class of potential games.

No abstract available.

Demand response is a crucial aspect of the future smart grid. It has the potential to provide significant peak demand reduction and to ease the incorporation of renewable energy into the grid. Data centers' participation in demand response is becoming increasingly important given the high and increasing energy consumption and the flexibility in demand management in data centers compared to conventional industrial facilities. In this extended abstract we briefly describe recent work in our full paper on two demand response schemes to reduce a data center's peak loads and energy expenditure: workload shifting and the use of local power generations. In our full paper, we conduct a detailed characterization study of coincident peak data over two decades from Fort Collins Utilities, Colorado and then develop two algorithms for data centers by combining workload scheduling and local power generation to avoid the coincident peak and reduce the energy expenditure. The first algorithm optimizes the expected cost and the second one provides a good worst-case guarantee for any coincident peak pattern. We evaluate these algorithms via numerical simulations based on real world traces from production systems. The results show that using workload shifting in combination with local generation can provide significant cost savings (up to 40% in the Fort Collins Utilities' case) compared to either alone.

Heavy-tails are a continual source of excitement and confusion across disciplines as they are repeatedly "discovered" in new contexts. This is especially true within computer systems, where heavy-tails seemingly pop up everywhere -- from degree distributions in the internet and social networks to file sizes and interarrival times of workloads. However, despite nearly a decade of work on heavy-tails they are still treated as mysterious, surprising, and even controversial.

Power consumption imposes a significant cost for data centers implementing cloud services, yet much of that power is used to maintain excess service capacity during periods of low load. This paper investigates how much can be saved by dynamically “right-sizing” the data center by turning off servers during such periods and how to achieve that saving via an online algorithm. We propose a very general model and prove that the optimal offline algorithm for dynamic right-sizing has a simple structure when viewed in reverse time, and this structure is exploited to develop a new “lazy” online algorithm, which is proven to be 3-competitive. We validate the algorithm using traces from two real data-center workloads and show that significant cost savings are possible. Additionally, we contrast this new algorithm with the more traditional approach of receding horizon control.

In this work, we study the complexity of finding a Walrasian equilibrium. Our main result gives an algorithm which can compute an approximate Walrasian equilibrium in an exchange economy with general, but well-behaved, utility functions in time that is polynomial in the number of goods when the number of agents is held constant. This result has applications to macroeconomics and finance, where applications of Walrasian equilibrium theory tend to deal with many goods but a fixed number of agents.

Recently, the demand for data center computing has surged, increasing the total energy footprint of data centers worldwide. Data centers typically comprise three subsystems: IT equipment provides services to customers; power infrastructure supports the IT and cooling equipment; and the cooling infrastructure removes heat generated by these subsystems. This work presents a novel approach to model the energy flows in a data center and optimize its operation. Traditionally, supply-side constraints such as energy or cooling availability were treated independently from IT workload management. This work reduces electricity cost and environmental impact using a holistic approach that integrates renewable supply, dynamic pricing, and cooling supply including chiller and outside air cooling, with IT workload planning to improve the overall sustainability of data center operations. Specifically, we first predict renewable energy as well as IT demand. Then we use these predictions to generate an IT workload management plan that schedules IT workload and allocates IT resources within a data center according to time varying power supply and cooling efficiency. We have implemented and evaluated our approach using traces from real data centers and production systems. The results demonstrate that our approach can reduce both the recurring power costs and the use of non-renewable energy by as much as 60% compared to existing techniques, while still meeting the Service Level Agreements.

Energy consumption imposes a significant cost for data centers; yet much of that energy is used to maintain excess service capacity during periods of predictably low load. Resultantly, there has recently been interest in developing designs that allow the service capacity to be dynamically resized to match the current workload. However, there is still much debate about the value of such approaches in real settings. In this paper, we show that the value of dynamic resizing is highly dependent on statistics of the workload process. In particular, both slow time-scale non-stationarities of the workload (e.g., the peak-to-mean ratio) and the fast time-scale stochasticity (e.g., the burstiness of arrivals) play key roles. To illustrate the impact of these factors, we combine optimization-based modeling of the slow time-scale with stochastic modeling of the fast time scale. Within this framework, we provide both analytic and numerical results characterizing when dynamic resizing does (and does not) provide benefits.

Power consumption imposes a significant cost for data centers implementing cloud services, yet much of that power is used to maintain excess service capacity during periods of predictably low load. This paper investigates how much can be saved by dynamically `right-sizing' the data center by turning off servers during such periods, and how to achieve that saving via an online algorithm. We prove that the optimal offline algorithm for dynamic right-sizing has a simple structure when viewed in reverse time, and this structure is exploited to develop a new `lazy' online algorithm, which is proven to be 3-competitive. We validate the algorithm using traces from two real data center workloads and show that significant cost-savings are possible.

Recent results in complexity theory suggest that various economic theories require agents to solve computationally intractable problems. However, such results assume the agents are optimizing explicit utility functions, whereas the economic theories merely assume the agents behave rationally, where rational behavior is defined via some optimization problem. Might making rational choices be easier than solving the corresponding optimization problem? For at least one major economic theory, the theory of the consumer (which simply postulates that consumers are utility maximizing), we find this is indeed the case. In other words, we prove the possibly surprising result that computational constraints have no empirical consequences for consumer choice theory.

Energy expenditure has become a significant fraction of data center operating costs. Recently, "geographical load balancing" has been suggested to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energy use.

This work examines fundamental tradeoffs incurred by a speed scaler seeking to minimize the sum of expected response time and energy use per job. We prove that a popular speed scaler is 2-competitive for this objective and no "natural" speed scaler can do better. Additionally, we prove that energy-proportional speed scaling works well for both Shortest Remaining Processing Time (SRPT) and Processor Sharing (PS) and we show that under both SRPT and PS, gated-static speed scaling is nearly optimal when the mean workload is known, but that dynamic speed scaling provides robustness against uncertain workloads. Finally, we prove that speed scaling magnifies unfairness under SRPT but that PS remains fair under speed scaling. These results show that these speed scalers can achieve any two, but only two, of optimality, fairness, and robustness.

Load balancing is a common approach for task assignment in distributed architectures. In this paper, we show that the degree of inefficiency in load balancing designs is highly dependent on the scheduling discipline used at each of the back-end servers. Traditionally, the back-end scheduler can be modeled as processor sharing (PS), in which case the degree of inefficiency grows linearly with the number of servers. However, if the back- end scheduler is changed to shortest remaining processing time (SRPT), the degree of inefficiency can be independent of the number of servers, instead depending only on the heterogeneity of the speeds of the servers. Further, switching the back-end scheduler to SRPT can provide significant improvements in the overall mean response time of the system as long as the heterogeneity of the server speeds is small.

Energy use of computer communication systems has quickly become a vital design consideration. One effective method for reducing energy consumption is dynamic speed scaling, which adapts the processing speed to the current load. This paper studies how to optimally scale speed to balance mean response time and mean energy consumption under processor sharing scheduling. Both bounds and asymptotics for the optimal speed scaling scheme are provided. These results show that a simple scheme that halts when the system is idle and uses a static rate while the system is busy provides nearly the same performance as the optimal dynamic speed scaling. However, the results also highlight that dynamic speed scaling provides at least one key benefit - significantly improved robustness to bursty traffic and mis-estimation of workload parameters.

Motivated by the optimality of Shortest Remaining Processing Time (SRPT) for mean response time, in recent years many computer systems have used the heuristic of "favoring small jobs" in order to dramatically reduce user response times. However, rarely do computer systems have knowledge of exact remaining sizes. In this paper, we introduce the class of ε-SMART policies, which formalizes the heuristic of "favoring small jobs" in a way that includes a wide range of policies that schedule using inexact job-size information. Examples of ε-SMART policies include (i) policies that use exact size information, e.g., SRPT and PSJF, (ii) policies that use job-size estimates, and (iii) policies that use a finite number of size-based priority levels.

Scheduling/prioritization of DBMS transactions is important for many applications that rely on database backends. A convenient way to achieve scheduling is to limit the number of transactions within the database, maintaining most of the transactions in an external queue, which can be ordered as desired by the application. While external scheduling has many advantages in that it doesn’t require changes to internal resources, it is also difficult to get right in that its performance depends critically on the particular multiprogramming limit used (the MPL), i.e. the number of transactions allowed into the database. If the MPL is too low, throughput will suffer, since not all DBMS resources will be utilized. On the other hand, if the MPL is too high, there is insufficient control on scheduling. The question of how to adjust theMPL to achieve both goals simultaneously is an open problem, not just for databases but in system design in general. Herein we study this problem in the context of transactional workloads, both via extensive experimentation and queueing theoretic analysis. We find that the two most critical factors in adjusting the MPL are the number of resources that the workload utilizes and the variability of the transactions’ service demands. We develop a feedback based controller, augmented by queueing theoretic models for automatically adjusting the MPL. Finally, we apply our methods to the specific problem of external prioritization of transactions. We find that external prioritization can be nearly as effective as internal prioritization, without any negative consequences, when the MPL is set appropriately.

In addition to providing small mean response times, modern applications seek to provide users predictable service and, in some cases, Quality of Service (QoS) guarantees. In order to understand the predictability of response times under a range of scheduling policies, we study the conditional variance in response times seen by jobs of different sizes. We define a metric and a criterion that distinguish between contrasting functional behaviors of conditional variance, and we then classify large groups of scheduling policies.In addition to studying the conditional variance of response times, we also derive metrics appropriate for comparing higher conditional moments of response time across job sizes. We illustrate that common statistics such as raw and central moments are not appropriate when comparing higher conditional moments of response time. Instead, we find that cumulant moments should be used.

We define the class of SMART scheduling policies. These are policies that bias towards jobs with small remaining service times, jobs with small original sizes, or both, with the motivation of minimizing mean response time and/or mean slowdown. Examples of SMART policies include PSJF, SRPT, and hybrid policies such as RS (which biases according to the product of the remaining size and the original size of a job).For many policies in the SMART class, the mean response time and mean slowdown are not known or have complex representations involving multiple nested integrals, making evaluation difficult. In this work, we prove three main results. First, for all policies in the SMART class, we prove simple upper and lower bounds on mean response time. Second, we show that all policies in the SMART class, surprisingly, have very similar mean response times. Third, we show that the response times of SMART policies are largely insensitive to the variability of the job size distribution. In particular, we focus on the SRPT and PSJF policies and prove insensitive bounds in these cases.

In addition to providing small mean response times, modern applications seek to provide users predictable service and, in some cases, Quality of Service (QoS) guarantees. In order to understand the predictability of response times under a range of scheduling policies, we study the conditional variance in response times seen by jobs of different sizes. We define a metric and a criterion that distinguish between contrasting functional behaviors of conditional variance, and we then classify large groups of scheduling policies. In addition to studying the conditional variance of response times, we also derive metrics appropriate for comparing higher conditional moments of response time across job sizes. We illustrate that common statistics such as raw and central moments are not appropriate when comparing higher conditional moments of response time. Instead, we find that cumulant moments should be used.