Offline Imitation of Badminton Player Behavior via Experiential Contexts and Brownian Motion

In the dynamic and rapid tactic involvements of turn-based sports, badminton stands out as an intrinsic paradigm that requires alter-dependent decision-making of players. While the advancement of learning from offline expert data in sequential decision-making has been witnessed in various domains, how to rally-wise imitate the behaviors of human players from offline badminton matches has remained underexplored. Replicating opponents' behavior benefits players by allowing them to undergo strategic development with direction before matches. However, directly applying existing methods suffers from the inherent hierarchy of the match and the compounding effect due to the turn-based nature of players alternatively taking actions. In this paper, we propose RallyNet, a novel hierarchical offline imitation learning model for badminton player behaviors: (i) RallyNet captures players' decision dependencies by modeling decision-making processes as a contextual Markov decision process. (ii) RallyNet leverages the experience to generate context as the agent's intent in the rally. (iii) To generate more realistic behavior, RallyNet leverages Geometric Brownian Motion (GBM) to model the interactions between players by introducing a valuable inductive bias for learning player behaviors. In this manner, RallyNet links player intents with interaction models with GBM, providing an understanding of interactions for sports analytics. We extensively validate RallyNet with the largest available real-world badminton dataset consisting of men's and women's singles, demonstrating its ability to imitate player behaviors. Results reveal RallyNet's superiority over offline imitation learning methods and state-of-the-art turn-based approaches, outperforming them by at least 16% in mean rule-based agent normalization score. Furthermore, we discuss various practical use cases to highlight RallyNet's applicability.