A Novel Individually Rational Objective In Multi-Agent Multi-Armed Bandits: Algorithms and Regret Bounds

We study a two-player stochastic multi-armed bandit (MAB) problem with different expected rewards for each player, a generalisation of two-player general sum repeated games to stochastic rewards. 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 main contribution is the derivation of an algorithm, UCRG, that achieves simultaneously for both players, a high-probability regret bound of order Õ (T2/3) after any T rounds of play. We demonstrate that our upper bound is nearly optimal by proving a lower bound of (T2/3) for any algorithm. Experiments confirm our theoretical results and the superiority of UCRG compared to the well-known explore-then-commit heuristic.