Near-Optimal Online Egalitarian learning in General Sum Repeated Matrix Games
This work addresses the challenge of fair and efficient learning in repeated games for multi-agent systems, representing a strong specific gain rather than a broad breakthrough.
The paper tackles the problem of finding the egalitarian bargaining solution in two-player general sum repeated finite games with unknown reward distributions, achieving a high-probability regret bound of O(∛(ln T)·T^{2/3}) for both players, which is shown to be nearly optimal with a lower bound of Ω(T^{2/3}).
We study two-player general sum repeated finite games where the rewards of each player are generated from an unknown distribution. Our aim is to find the egalitarian bargaining solution (EBS) for the repeated game, which can lead to much higher rewards than the maximin value of both players. Our most important contribution is the derivation of an algorithm that achieves simultaneously, for both players, a high-probability regret bound of order $\mathcal{O}(\sqrt[3]{\ln T}\cdot T^{2/3})$ after any $T$ rounds of play. We demonstrate that our upper bound is nearly optimal by proving a lower bound of $Ω(T^{2/3})$ for any algorithm.