Bayesian Inverse Games with High-Dimensional Multi-Modal Observations

2026-01-02

arXiv.org

AI Summary

This work addresses the challenge of uncertainty quantification in inverse game theory for non-cooperative multi-agent systems, where conventional approaches yield only point estimates of agents’ objective functions, often leading to overconfident downstream decisions. To overcome this limitation, we introduce a novel approximate Bayesian framework that, for the first time, integrates Bayesian inference into inverse game problems. Our method leverages a structured variational autoencoder coupled with an embedded differentiable Nash equilibrium solver to unsupervisedly infer the full posterior distribution over agents’ objectives from high-dimensional, multimodal observations. The framework naturally supports multimodal observation fusion and remains effective even under partial trajectory information, substantially reducing epistemic uncertainty and enhancing decision safety and robustness. Experimental results demonstrate clear superiority over existing maximum-likelihood baselines.

Technology Category

• Multiagent Systems: Adversarial Agents
• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Bayesian inverse games
• multi-agent interaction
• objective inference
• uncertainty quantification
• multi-modal observations

Innovation

• Bayesian inverse games
• multimodal observations
• structured variational autoencoder
• differentiable Nash solver
• uncertainty quantification