Efficient Episodic Learning of Nonstationary and Unknown Zero-Sum Games Using Expert Game Ensembles

Abstract: Game theory provides essential analysis in many applications of strategic interactions. However, the question of how to construct a game model and what is its fidelity is seldom addressed. In this work, we consider learning in a class of repeated zero-sum games with unknown, time-varying payoff matrix, and noisy feedbacks, by making use of an ensemble of benchmark game models. These models can be pre-trained and collected dynamically during sequential plays. They serve as prior side information and imperfectly underpin the unknown true game model. We propose OFULinMat, an episodic learning algorithm that integrates the adaptive estimation of game models and the learning of the strategies. The proposed algorithm is shown to achieve a sublinear bound on the saddle-point regret. We show that this algorithm is provably efficient through both theoretical analysis and numerical examples. We use a dynamic honeypot allocation game as a case study to illustrate and corroborate our results. We also discuss the relationship and highlight the difference between our framework and the classical adversarial multi-armed bandit framework.