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.

翻译：博弈论为建模多智能体交互提供了可解释的数学框架。然而，其在现实机器人应用中的适用性受到诸如未知智能体偏好与目标等挑战的限制。为应对这些挑战，我们揭示了微分博弈、最优控制与能量模型之间的联系，并展示了现有方法如何在我们提出的能量势博弈框架下得到统一。基于该框架，本文引入一种新型端到端学习应用，将神经网络用于博弈参数推断，并与可微的博弈论优化层相结合，作为归纳偏置。通过模拟移动机器人行人交互与真实自动驾驶数据的实验，经验证据表明，该博弈论优化层提升了多种神经网络骨干结构的预测性能。