Bayesian Inverse Games with High-Dimensional Multi-Modal Observations

Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a specification of all agents' objectives. To circumvent this practical difficulty, recent work develops maximum likelihood techniques for solving inverse games that can identify unknown agent objectives from interaction data. Unfortunately, these methods only infer point estimates and do not quantify estimator uncertainty; correspondingly, downstream planning decisions can overconfidently commit to unsafe actions. We present an approximate Bayesian inference approach for solving the inverse game problem, which can incorporate observation data from multiple modalities and be used to generate samples from the Bayesian posterior over the hidden agent objectives given limited sensor observations in real time. Concretely, the proposed Bayesian inverse game framework trains a structured variational autoencoder with an embedded differentiable Nash game solver on interaction datasets and does not require labels of agents' true objectives. Extensive experiments show that our framework successfully learns prior and posterior distributions, improves inference quality over maximum likelihood estimation-based inverse game approaches, and enables safer downstream decision-making without sacrificing efficiency. When trajectory information is uninformative or unavailable, multimodal inference further reduces uncertainty by exploiting additional observation modalities.