R2-B2: Recursive Reasoning-Based Bayesian Optimization for No-Regret Learning in Games
This work addresses the challenge of efficient learning in multi-agent games with complex payoff functions, which is incremental as it builds on Bayesian optimization and recursive reasoning methods.
The paper tackled the problem of modeling interactions between boundedly rational agents with unknown payoff functions in repeated games by introducing a recursive reasoning formalism of Bayesian optimization called R2-B2, proving that it achieves faster asymptotic convergence to no regret and demonstrating its performance in synthetic games, adversarial machine learning, and multi-agent reinforcement learning.
This paper presents a recursive reasoning formalism of Bayesian optimization (BO) to model the reasoning process in the interactions between boundedly rational, self-interested agents with unknown, complex, and costly-to-evaluate payoff functions in repeated games, which we call Recursive Reasoning-Based BO (R2-B2). Our R2-B2 algorithm is general in that it does not constrain the relationship among the payoff functions of different agents and can thus be applied to various types of games such as constant-sum, general-sum, and common-payoff games. We prove that by reasoning at level 2 or more and at one level higher than the other agents, our R2-B2 agent can achieve faster asymptotic convergence to no regret than that without utilizing recursive reasoning. We also propose a computationally cheaper variant of R2-B2 called R2-B2-Lite at the expense of a weaker convergence guarantee. The performance and generality of our R2-B2 algorithm are empirically demonstrated using synthetic games, adversarial machine learning, and multi-agent reinforcement learning.