Exploiting Opponents Under Utility Constraints in Sequential Games

Recently, game-playing agents based on AI techniques have demonstrated super-human performance in several sequential games, such as chess, Go, and poker. Surprisingly, the multi-agent learning techniques that allowed to reach these achievements do not take into account the actual behavior of the human player, potentially leading to an impressive gap in performances. In this paper, we address the problem of designing artificial agents that learn how to effectively exploit unknown human opponents while playing repeatedly against them in an online fashion. We study the case in which the agent's strategy during each repetition of the game is subject to constraints ensuring that the human's expected utility is within some lower and upper thresholds. Our framework encompasses several real-world problems, such as human engagement in repeated game playing and human education by means of serious games. As a first result, we formalize a set of linear inequalities encoding the conditions that the agent's strategy must satisfy at each iteration in order to do not violate the given bounds for the human's expected utility. Then, we use such formulation in an upper confidence bound algorithm, and we prove that the resulting procedure suffers from sublinear regret and guarantees that the constraints are satisfied with high probability at each iteration. Finally, we empirically evaluate the convergence of our algorithm on standard testbeds of sequential games.