  Dynamically planning in complex systems has been explored to improve
decision-making in various domains. Professional basketball serves as a
compelling example of a dynamic spatio-temporal game, encompassing
context-dependent decision-making. However, processing the diverse on-court
signals and navigating the vast space of potential actions and outcomes make it
difficult for existing approaches to swiftly identify optimal strategies in
response to evolving circumstances. In this study, we formulate the sequential
decision-making process as a conditional trajectory generation process. Based
on the formulation, we introduce PlayBest (PLAYer BEhavior SynThesis), a method
to improve player decision-making. We extend the diffusion probabilistic model
to learn challenging environmental dynamics from historical National Basketball
Association (NBA) player motion tracking data. To incorporate data-driven
strategies, an auxiliary value function is trained with corresponding rewards.
To accomplish reward-guided trajectory generation, we condition the diffusion
model on the value function via classifier-guided sampling. We validate the
effectiveness of PlayBest through simulation studies, contrasting the generated
trajectories with those employed by professional basketball teams. Our results
reveal that the model excels at generating reasonable basketball trajectories
that produce efficient plays. Moreover, the synthesized play strategies exhibit
an alignment with professional tactics, highlighting the model's capacity to
capture the intricate dynamics of basketball games.
