S Jecmen, A Sinha, Z Li, L Tran-Thanh
Empirical game-theoretic analysis refers to a set of models and techniques for solving large-scale games. However, there is a lack of a quantitative guarantee about the quality of output approximate Nash equilibria (NE). A natural quantitative guarantee for such an approximate NE is the regret in the game (i.e. the best deviation gain). We formulate this deviation gain computation as a multi-armed bandit problem, with a new optimization goal unlike those studied in prior work. We propose an efficient algorithm Super-Arm UCB (SAUCB) for the problem and a number of variants. We present sample complexity results as well as extensive experiments that show the better performance of SAUCB compared to several baselines.
A preliminary version of this paper, titled “Bounding Regret in Simulated Games” and authored by S Jecmen, E Brinkman, and A Sinha, was presented at the ICML-18 Workshop on Exploration in RL, July 2018.