Communication Efficient Decentralization for Smoothed Online Convex Optimization

We study the multi-agent Smoothed Online Convex Optimization (SOCO) problem, where $N$ agents interact through a communication graph. In each round, each agent $i$ receives a strongly convex hitting cost function $f^i_t$ in an online fashion and selects an action $x^i_t \in \mathbb{R}^d$. The objective is to minimize the global cumulative cost, which includes the sum of individual hitting costs $f^i_t(x^i_t)$, a temporal "switching cost" for changing decisions, and a spatial "dissimilarity cost" that penalizes deviations in decisions among neighboring agents. We propose the first decentralized algorithm for multi-agent SOCO and prove its asymptotic optimality. Our approach allows each agent to operate using only local information from its immediate neighbors in the graph. For finite-time performance, we establish that the optimality gap in competitive ratio decreases with the time horizon $T$ and can be conveniently tuned based on the per-round computation available to each agent. Moreover, our results hold even when the communication graph changes arbitrarily and adaptively over time. Finally, we establish that the computational complexity per round depends only logarithmically on the number of agents and almost linearly on their degree within the graph, ensuring scalability for large-system implementations.

Safe Exploitative Play with Untrusted Type Beliefs

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.

Hybrid Transfer Reinforcement Learning: Provable Sample Efficiency from Shifted-Dynamics Data

Online Reinforcement learning (RL) typically requires high-stakes online interaction data to learn a policy for a target task. 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, with prior information on the degree of the dynamics shift, we design HySRL, a transfer algorithm that achieves problem-dependent sample complexity and outperforms pure online RL. Finally, our experimental results demonstrate that HySRL surpasses state-of-the-art online RL baseline.

Online Budgeted Matching with General Bids

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.

Can We Break the Curse of Multiagency in Robust Multi-Agent Reinforcement Learning?

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. Solving RMGs remains under-explored, from problem formulation to the development of sample-efficient algorithms. A notorious yet open challenge is if RMGs can escape 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 where the uncertainty set of each agent is shaped by both the environment and other agents' strategies in a best-response manner. We first establish the well-posedness of these 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.

End-to-End Conformal Calibration for Optimization Under Uncertainty

Machine learning can significantly improve performance for decision-making under uncertainty in a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve in high-capacity prediction models such as deep neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with their own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn the uncertainty estimates for conditional robust optimization, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent arbitrary convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization.

Last-Iterate Convergence of Payoff-Based Independent Learning in Zero-Sum Stochastic Games

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix games are based on the smoothed best-response dynamics, while the learning dynamics for stochastic games build upon those for matrix games, with additional incorporation of the minimax value iteration. To our knowledge, our theoretical results present the first finite-sample analysis of such learning dynamics with last-iterate guarantees. In the matrix game setting, the results imply a sample complexity of $O(\epsilon^{-1})$ to find the Nash distribution and a sample complexity of $O(\epsilon^{-8})$ to find a Nash equilibrium. In the stochastic game setting, the results also imply a sample complexity of $O(\epsilon^{-8})$ to find a Nash equilibrium. To establish these results, the main challenge is to handle stochastic approximation algorithms with multiple sets of coupled and stochastic iterates that evolve on (possibly) different time scales. To overcome this challenge, we developed a coupled Lyapunov-based approach, which may be of independent interest to the broader community studying the convergence behavior of stochastic approximation algorithms.

CarbonClipper: Optimal Algorithms for Carbon-Aware Spatiotemporal Workload Management

We study carbon-aware spatiotemporal workload management, which seeks to address the growing environmental impact of data centers. We formalize this as an online problem called spatiotemporal online allocation with deadline constraints ($\mathsf{SOAD}$), in which an online player completes a workload (e.g., a batch compute job) by moving and scheduling the workload across a network subject to a deadline $T$. At each time step, a service cost function is revealed, representing, e.g., the carbon intensity of servicing a workload at each location, and the player must irrevocably decide the current allocation. Furthermore, whenever the player moves the allocation, it incurs a movement cost defined by a metric space $(X,d)$ that captures, e.g., the overhead of migrating a compute job. $\mathsf{SOAD}$ formalizes the open problem of combining general metrics and deadline constraints in the online algorithms literature, unifying problems such as metrical task systems and online search. We propose a competitive algorithm for $\mathsf{SOAD}$ along with a matching lower bound that proves it is optimal. Our main algorithm, ${\rm C{\scriptsize ARBON}C{\scriptsize LIPPER}}$, is a learning-augmented algorithm that takes advantage of predictions (e.g., carbon intensity forecasts) and achieves an optimal consistency-robustness trade-off. We evaluate our proposed algorithms for carbon-aware spatiotemporal workload management on a simulated global data center network, showing that ${\rm C{\scriptsize ARBON}C{\scriptsize LIPPER}}$ significantly improves performance compared to baseline methods and delivers meaningful carbon reductions.

Distributionally Robust Constrained Reinforcement Learning under Strong Duality

We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and testing environments differ, and policies must satisfy constraints motivated by safety or limited budgets. Despite significant progress toward algorithm design for the separate problems of distributionally robust RL and constrained RL, there do not yet exist algorithms with end-to-end convergence guarantees for DRC-RL. We develop an algorithmic framework based on strong duality that enables the first efficient and provable solution in a class of environmental uncertainties. Further, our framework exposes an inherent structure of DRC-RL that arises from the combination of distributional robustness and constraints, which prevents a popular class of iterative methods from tractably solving DRC-RL, despite such frameworks being applicable for each of distributionally robust RL and constrained RL individually. Finally, we conduct experiments on a car racing benchmark to evaluate the effectiveness of the proposed algorithm.

Enhancing Efficiency of Safe Reinforcement Learning via Sample Manipulation

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%.