Related papers: On the Variational Interpretation of Mirror Play i…
Markov Potential Games (MPGs) form an important sub-class of Markov games, which are a common framework to model multi-agent reinforcement learning problems. In particular, MPGs include as a special case the identical-interest setting where…
Learning in multi-player games can model a large variety of practical scenarios, where each player seeks to optimize its own local objective function, which at the same time relies on the actions taken by others. Motivated by the frequent…
This paper proposes a payoff perturbation technique for the Mirror Descent (MD) algorithm in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. The optimistic…
Policy Mirror Descent (PMD) is a popular framework in reinforcement learning, serving as a unifying perspective that encompasses numerous algorithms. These algorithms are derived through the selection of a mirror map and enjoy finite-time…
Markov games (MGs) provide a mathematical foundation for multi-agent reinforcement learning (MARL), enabling self-interested agents to learn their optimal policies while interacting with others in a shared environment. However, due to the…
Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…
In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS)…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like…
In this paper, we provide exponential rates of convergence to the interior Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in $N$-player continuous…
We examine the long-run behavior of multi-agent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to Nash…
Mean-field games have been used as a theoretical tool to obtain an approximate Nash equilibrium for symmetric and anonymous $N$-player games. However, limiting applicability, existing theoretical results assume variations of a "population…
We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity…
Certain but important classes of strategic-form games, including zero-sum and identical-interest games, have the fictitious-play-property (FPP), i.e., beliefs formed in fictitious play dynamics always converge to a Nash equilibrium (NE) in…
We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization…
Potential games are arguably one of the most important and widely studied classes of normal form games. They define the archetypal setting of multi-agent coordination as all agent utilities are perfectly aligned with each other via a common…
Mirror-prox (MP) is a well-known algorithm to solve variational inequality (VI) problems. VI with a monotone operator covers a large group of settings such as convex minimization, min-max or saddle point problems. To get a convergent…
Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…
We study Nash equilibria learning of a general-sum stochastic game with an unknown transition probability density function. Agents take actions at the current environment state and their joint action influences the transition of the…