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多挑战的制约，例如智能体的偏好与目标未知。为应对这些挑战，本文揭示了微分博弈、最优控制与能量模型之间的联系，并展示了现有方法如何统一于我们提出的基于能量的势博弈框架。基于这一框架，本文引入了一种全新的端到端学习应用，该应用将用于博弈参数推理的神经网络与可微分的博弈论优化层相结合，该优化层充当归纳偏置。基于仿真移动机器人行人交互以及真实自动驾驶数据的实验表明，博弈论优化层能够提升多种神经网络主干结构的预测性能。