An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility of regret minimization under the assumption that all parties adopt the same learning procedure. In this work, we present the first (to our knowledge) algorithm for learning in general-sum Markov games that provides sublinear regret guarantees when executed by all agents. The bounds we obtain are for swap regret, and thus, along the way, imply convergence to a correlated equilibrium. Our algorithm is decentralized, computationally efficient, and does not require any communication between agents. Our key observation is that online learning via policy optimization in Markov games essentially reduces to a form of weighted regret minimization, with unknown weights determined by the path length of the agents' policy sequence. Consequently, controlling the path length leads to weighted regret objectives for which sufficiently adaptive algorithms provide sublinear regret guarantees.

简而言之，本文提出了一种针对广义和博弈的、分散、计算高效的算法，其保证所有代理都使用时可以提供次线性遗憾保证，并且不需要代理之间的通信。该算法的主要观察结果是，通过马尔可夫游戏的在线学习基本上可以归结为一种加权遗憾最小化。

一般和式马尔可夫博弈的遗憾最小化和均衡收敛