When multiple agents interact in a common environment, each agent's actions
impact others' future decisions, and noncooperative dynamic games naturally
capture this coupling. In interactive motion planning, however, agents
typically do not have access to a complete model of the game, e.g., due to
unknown objectives of other players. Therefore, we consider the inverse game
problem, in which some properties of the game are unknown a priori and must be
inferred from observations. Existing maximum likelihood estimation (MLE)
approaches to solve inverse games provide only point estimates of unknown
parameters without quantifying uncertainty, and perform poorly when many
parameter values explain the observed behavior. To address these limitations,
we take a Bayesian perspective and construct posterior distributions of game
parameters. To render inference tractable, we employ a variational autoencoder
(VAE) with an embedded differentiable game solver. This structured VAE can be
trained from an unlabeled dataset of observed interactions, naturally handles
continuous, multi-modal distributions, and supports efficient sampling from the
inferred posteriors without computing game solutions at runtime. Extensive
evaluations in simulated driving scenarios demonstrate that the proposed
approach successfully learns the prior and posterior objective distributions,
provides more accurate objective estimates than MLE baselines, and facilitates
safer and more efficient game-theoretic motion planning.

基于贝叶斯观点和变分自编码器，提出一种解决交互式运动规划中的逆游戏问题的方法，通过构建后验分布来量化未知参数的不确定性，并且在处理连续、多模态分布时具有高效性。在模拟驾驶场景中的广泛评估中表明，该方法成功学习先验和后验目标分布，相比 MLE 基准，提供更准确的目标估计，从而促进更安全、更高效的博弈论运动规划。