$\widetilde{O}(T^{-1})$ Convergence to (Coarse) Correlated Equilibria in Full-Information General-Sum Markov Games
This work addresses a gap in convergence rates for equilibrium solutions in Markov games, which is foundational for multi-agent reinforcement learning, though it is incremental as it extends existing no-regret learning dynamics to a more generic setting.
The paper tackles the problem of achieving fast convergence to (coarse) correlated equilibria in full-information general-sum Markov games, a key setting in multi-agent reinforcement learning, by showing that the optimistic-follow-the-regularized-leader algorithm with value updates achieves an $\widetilde{O}(T^{-1})$ approximate equilibrium within $T$ iterations, improving over the classic $O(1/\sqrt{T})$ rate.
No-regret learning has a long history of being closely connected to game theory. Recent works have devised uncoupled no-regret learning dynamics that, when adopted by all the players in normal-form games, converge to various equilibrium solutions at a near-optimal rate of $\widetilde{O}(T^{-1})$, a significant improvement over the $O(1/\sqrt{T})$ rate of classic no-regret learners. However, analogous convergence results are scarce in Markov games, a more generic setting that lays the foundation for multi-agent reinforcement learning. In this work, we close this gap by showing that the optimistic-follow-the-regularized-leader (OFTRL) algorithm, together with appropriate value update procedures, can find $\widetilde{O}(T^{-1})$-approximate (coarse) correlated equilibria in full-information general-sum Markov games within $T$ iterations. Numerical results are also included to corroborate our theoretical findings.