Regret Minimization and Convergence to Equilibria in General-sum Markov Games
This addresses the challenge of learning in multi-agent systems for researchers in game theory and reinforcement learning, offering a novel solution to a previously intractable problem.
The authors tackled the problem of regret minimization in general-sum Markov games, presenting the first decentralized algorithm that achieves sublinear swap regret when all agents use it, implying convergence to correlated equilibrium without communication.
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.