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The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects…

We consider the setting where players run the Hedge algorithm or its optimistic variant to play an $n$-action game repeatedly for $T$ rounds. 1) For two-player games, we show that the regret of optimistic Hedge decays at $\tilde{O}( 1/T…

In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining both sublinear regret and sublinear constraint violation, when competing…

We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to…

We consider the problem where $M$ agents interact with $M$ identical and independent environments with $S$ states and $A$ actions using reinforcement learning for $T$ rounds. The agents share their data with a central server to minimize…

This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…

We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter…

We study the limiting behavior of the mixed strategies that result from optimal no-regret learning strategies in a repeated game setting where the stage game is any 2 by 2 competitive game. We consider optimal no-regret algorithms that are…

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost…

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called…

We study the problem of full-information online learning in the "bounded recall" setting popular in the study of repeated games. An online learning algorithm $\mathcal{A}$ is $M$-$\textit{bounded-recall}$ if its output at time $t$ can be…

We study an asynchronous online learning setting with a network of agents. At each time step, some of the agents are activated, requested to make a prediction, and pay the corresponding loss. The loss function is then revealed to these…

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

In this paper, we consider the problem of finding a meta-learning online control algorithm that can learn across the tasks when faced with a sequence of $N$ (similar) control tasks. Each task involves controlling a linear dynamical system…

We study learnability of mixed-strategy Nash Equilibrium (NE) in general finite games using higher-order replicator dynamics as well as classes of higher-order uncoupled heterogeneous dynamics. In higher-order uncoupled learning dynamics,…

A central capability of intelligent systems is the ability to continuously build upon previous experiences to speed up and enhance learning of new tasks. Two distinct research paradigms have studied this question. Meta-learning views this…

We present a new algorithm based on posterior sampling for learning in constrained Markov decision processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous…

This paper studies the optimistic variant of Fictitious Play for learning in two-player zero-sum games. While it is known that Optimistic FTRL -- a regularized algorithm with a bounded stepsize parameter -- obtains constant regret in this…

We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret…

We study an online mixed discrete and continuous optimization problem where a decision maker interacts with an unknown environment for a number of $T$ rounds. At each round, the decision maker needs to first jointly choose a discrete and a…