Bayesian Inverse Games with High-Dimensional Multi-Modal Observations

TL;DR

This work tackles inverse dynamic games where $N$ agents interact noncooperatively and the opponents’ objectives $\theta$ are unknown. It introduces a Bayesian inverse-game framework that fuses multimodal observations (trajectories and images) via a structured variational autoencoder with a differentiable Nash solver, enabling real-time sampling from $p(\theta\mid y)$. The model is trained offline on unlabeled interaction data and can produce multimodal posterior samples online, improving planning safety and efficiency compared with mle-based baselines, especially when trajectory information is scarce. Experiments in simulated intersections and CARLA-based scenarios show that multimodal context reduces posterior uncertainty and yields safer, smoother motion planning.

Abstract

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.

Figures (14)

• Figure 1: A robot interacts with an opponent driver whose goal position is unknown. We embed a differentiable game solver within a structured variational autoencoder to infer the distribution of opponent intent from observed trajectories, jointly with image observations of the opponent.
• Figure 2: Bayes network representation of our latent variable model relating the observed image ${y_\mathrm{img}}$ and trajectory ${y_\text{traj}}$ to the game parameters $\theta$ via a latent variable $z$. Note that, by construction, the observed image ${y_\mathrm{img}}$ and trajectory ${y_\text{traj}}$ are statistically dependent but conditionally independent, given latent variable $z$.
• Figure 3: Overview of a structured vae for generative Bayesian inverse games.
• Figure 4: Snapshots from an intersection scenario (\ref{['sec:intersection-state-obs']}) in which the ego robot is controlled by our bpine approach (top) and the R-mle baseline (bottom). For R-mle, the estimated goal is shown as a green star whose size increases over time. Reproduced from conference publication liu2024auto.
• Figure 5: mle inverse game cost landscape (negative observation log-likelihood, $-\log p(y \mid p^2_{\mathrm{goal}})$, over opponent goal positions $p^2_{\mathrm{goal}}$) for the R-mle baseline at time steps 27 and 46 of the interaction in \ref{['fig:intersection-qualitative']}. Because it ignores Bayesian priors, the mle inverse game problem can be ill-posed and exhibit a flat cost landscape; consequently, its solutions may induce unsafe downstream decisions (cf. \ref{['fig:intersection-qualitative']}). Reproduced from conference publication liu2024auto.

Theorems & Definitions (2)

• Remark 1
• Remark 2