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

TL;DR

This paper establishes a theoretical link between differential games, optimal control, and energy-based models to improve multi-agent interaction modeling, introducing a novel energy-based potential game framework and a neural network-based learning approach validated on robotics data.

Contribution

It proposes a unified energy-based potential game formulation connecting differential games and optimal control, and develops an end-to-end neural network method incorporating game-theoretic optimization for multi-agent systems.

Findings

Game-theoretic layer enhances predictive accuracy in robot interaction models.

The approach successfully integrates neural networks with game-theoretic optimization.

Empirical validation on simulated and real-world driving data shows improved performance.

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 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.