Regret Minimization and Convergence to Equilibria in General-sum Markov Games
Liad Erez,u00a0Tal Lancewicki,u00a0Uri Sherman,u00a0Tomer Koren,u00a0Yishay Mansour
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 $ extit{swap regret}$, and thus, along the way, imply convergence to a $ extit{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 $ extit{weighted}$ regret minimization, with $ extit{unknown}$ weights determined by the path length of the agentsu2019 policy sequence. Consequently, controlling the path length leads to weighted regret objectives for which sufficiently adaptive algorithms provide sublinear regret guarantees.
