Online Bayesian Learning of Agent Behavior in Differential Games

TL;DR

This paper presents an online Bayesian approach for real-time behavior identification in multi-agent systems, leveraging Hamilton-Jacobi-Bellman conditions to enable fast, uncertainty-aware predictions even with limited noisy data.

Contribution

It introduces a novel online Bayesian method that models agent behavior using linear-in-parameter residuals, accommodating nonlinear dynamics and providing real-time, uncertainty-aware inference.

Findings

Accurate behavior prediction in linear-quadratic scenarios

Effective handling of nonlinear dynamics with basis expansions

Quantified uncertainty improves adaptive decision making

Abstract

This work introduces an online Bayesian game-theoretic method for behavior identification in multi-agent dynamical systems. By casting Hamilton-Jacobi-Bellman optimality conditions as linear-in-parameter residuals, the method enables fast sequential Bayesian updates, uncertainty-aware inference, and robust prediction from limited, noisy data-without history stacks. The approach accommodates nonlinear dynamics and nonquadratic value functions through basis expansions, providing flexible models. Experiments, including linear-quadratic and nonlinear shared-control scenarios, demonstrate accurate prediction with quantified uncertainty, highlighting the method's relevance for adaptive interaction and real-time decision making.