Auto-Encoding Bayesian Inverse Games

TL;DR

Extensive evaluations in simulated driving scenarios demonstrate that the proposed approach successfully learns the prior and posterior game parameter distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.

Abstract

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 game parameter distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.

Figures (8)

• Figure 1: A robot interacting with a human driver whose goal position is unknown. We embed a differentiable game solver in a structured variational autoencoder to infer the distribution of the human's objectives based on observations of their behavior.
• Figure 2: Overview of a structured vae for generative Bayesian inverse games. Top (left to right): decoder pipeline. Bottom (right to left): variational inference via an encoder.
• Figure 3: Qualitative behavior of B-PinE (ours) vs. R-MLE. In the bottom row, the size of the green stars increases with time.
• Figure 4: Negative observation log-likelihood $-\log p(y \mid p^2_{\mathrm{goal}})$ for varying human goal positions $p^2_{\mathrm{goal}}$ at two time steps of the R-MLE trial in \ref{['fig:intersection-qualitative']}.
• Figure 5: Quantitative results of S1: (a) Minimum distance between agents in each trial. (b) Robot costs (with GT costs subtracted).