Preference-based opponent shaping in differentiable games

Abstract: Strategy learning in game environments with multi-agent is a challenging problem. Since each agent's reward is determined by the joint strategy, a greedy learning strategy that aims to maximize its own reward may fall into a local optimum. Recent studies have proposed the opponent modeling and shaping methods for game environments. These methods enhance the efficiency of strategy learning by modeling the strategies and updating processes of other agents. However, these methods often rely on simple predictions of opponent strategy changes. Due to the lack of modeling behavioral preferences such as cooperation and competition, they are usually applicable only to predefined scenarios and lack generalization capabilities. In this paper, we propose a novel Preference-based Opponent Shaping (PBOS) method to enhance the strategy learning process by shaping agents' preferences towards cooperation. We introduce the preference parameter, which is incorporated into the agent's loss function, thus allowing the agent to directly consider the opponent's loss function when updating the strategy. We update the preference parameters concurrently with strategy learning to ensure that agents can adapt to any cooperative or competitive game environment. Through a series of experiments, we verify the performance of PBOS algorithm in a variety of differentiable games. The experimental results show that the PBOS algorithm can guide the agent to learn the appropriate preference parameters, so as to achieve better reward distribution in multiple game environments.