On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions

Christopher Diehl, Tobias Klosek, Martin Krueger, Nils Murzyn, Torsten Bertram

Keywords: Trajectory Prediction, Game Theory, Optimal Control, Energy-based Models, Motion Forecasting, Differentiable Optimization

TL;DR: This work presents a connection between differential games, optimal control, and energy-based models and an application for multi-agent motion forecasting.

Abstract: Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and goals. To address these challenges, we show a connection between differential games, optimal control, and energy-based models and demonstrate how existing approaches can be unified under our proposed $\textit{Energy-based Potential Game}$ formulation. Building upon this formulation, this work introduces a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The experiments using simulated mobile robot pedestrian interactions and real-world automated driving data provide empirical evidence that the game-theoretic layer improves the predictive performance of various neural network backbones.

Submission Number: 42