Learning to Play Trajectory Games Against Opponents with Unknown Objectives

TL;DR

This paper introduces an adaptive, differentiable game solver for autonomous agents that infers opponents' objectives online, enabling real-time, robust trajectory planning in interactive scenarios with unknown objectives.

Contribution

It presents a novel differentiable trajectory game solver that jointly infers opponents' objectives and computes equilibrium strategies, handling partial observations and constraints.

Findings

Outperforms existing game-theoretic and MPC methods in simulated traffic scenarios.

Demonstrates real-time planning and robustness in hardware experiments.

Handles partial state observations and inequality constraints effectively.

Abstract

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two hardware experiments.