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In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the…

Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…

We study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with perfect information and simultaneous moves. We present a general template of MCTS algorithms for these games, which can be instantiated by various selection…

When Reinforcement Learning (RL) agents are deployed in practice, they might impact their environment and change its dynamics. We propose a new framework to model this phenomenon, where the current environment depends on the deployed policy…

We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions' cumulative payoffs over time - specifically, by playing mixed strategies that maximize their expected cumulative payoff…

The Nash Equilibrium (NE) assumes rational play in imperfect-information Extensive-Form Games (EFGs) but fails to ensure optimal strategies for off-equilibrium branches of the game tree, potentially leading to suboptimal outcomes in…

Our work focuses on extra gradient learning algorithms for finding Nash equilibria in bilinear zero-sum games. The proposed method, which can be formally considered as a variant of Optimistic Mirror Descent…

In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of…

We consider the Scale-Free Adversarial Multi Armed Bandits(MAB) problem. At the beginning of the game, the player only knows the number of arms $n$. It does not know the scale and magnitude of the losses chosen by the adversary or the…

Multi-agent robust reinforcement learning, also known as multi-player robust Markov games (RMGs), is a crucial framework for modeling competitive interactions under environmental uncertainties, with wide applications in multi-agent systems.…

We consider online linear optimization over symmetric positive semi-definite matrices, which has various applications including the online collaborative filtering. The problem is formulated as a repeated game between the algorithm and the…

We introduce two Smoothed Policy Iteration algorithms (\textbf{SPI}s) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling…

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a…

We investigate a nonstochastic bandit setting in which the loss of an action is not immediately charged to the player, but rather spread over the subsequent rounds in an adversarial way. The instantaneous loss observed by the player at the…

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we…

We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions nor sharing…

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…