Related papers: Geometrical Regret Matching
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
Correlated equilibrium generalizes Nash equilibrium by allowing a central coordinator to guide players' actions through shared recommendations, similar to how routing apps guide drivers. We investigate how a coordinator can learn a…
We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and…
In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…
We investigate the interplay between passivity, no-regret, and convergence in contractive games for various learning dynamic models and their higher-order variants. Our setting is continuous time. Building on prior work for replicator…
A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…
We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…
We study last-iterate convergence properties of algorithms for solving two-player zero-sum games based on Regret Matching$^+$ (RM$^+$). Despite their widespread use for solving real games, virtually nothing is known about their last-iterate…
Swap regret is a notion that has proven itself to be central to the study of general-sum normal-form games, with swap-regret minimization leading to convergence to the set of correlated equilibria and guaranteeing non-manipulability against…
Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…
Motivated by alternating learning dynamics in two-player games, a recent work by Cevher et al.(2024) shows that $o(\sqrt{T})$ alternating regret is possible for any $T$-round adversarial Online Linear Optimization (OLO) problem, and left as…
We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
We show that Optimistic Hedge -- a common variant of multiplicative-weights-updates with recency bias -- attains ${\rm poly}(\log T)$ regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic…
In zero-sum games, the optimal strategy is well-defined by the Nash equilibrium. However, it is overly conservative when playing against suboptimal opponents and it can not exploit their weaknesses. Limited look-ahead game solving in…
While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares…