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arXiv · 2308.16539

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

Christopher Diehl·Tobias Klosek·Martin Krüger·Nils Murzyn·Torsten Bertram
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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.

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Christopher Diehl, Tobias Klosek, Martin Krüger, Nils Murzyn, Torsten Bertram. 2023-08-31. On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions. https://arxiv.org/abs/2308.16539

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