Inverse Mixed Strategy Games with Generative Trajectory Models

TL;DR

This paper introduces a novel inverse game approach that uses a generative trajectory model with a CVAE to infer multi-modal, high-dimensional behaviors in noisy, uncertain multi-agent interactions, enabling real-time adaptation.

Contribution

It presents a differentiable inverse game method integrating a CVAE for high-dimensional behavior inference under noise and uncertainty, improving over existing approaches.

Findings

Accurately infers Nash-optimal actions despite model mismatch.

Performs well with noisy measurements and uncertain objectives.

Adapts in real-time to new observations.

Abstract

Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors -- a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.