The values of two-player general-sum differential games are viscosity
solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy
approximations for such games suffer from the curse of dimensionality (CoD).
Alleviating CoD through physics-informed neural networks (PINN) encounters
convergence issues when value discontinuity is present due to state
constraints. On top of these challenges, it is often necessary to learn
generalizable values and policies across a parametric space of games, e.g., for
game parameter inference when information is incomplete. To address these
challenges, we propose in this paper a Pontryagin-mode neural operator that
outperforms existing state-of-the-art (SOTA) on safety performance across games
with parametric state constraints. Our key contribution is the introduction of
a costate loss defined on the discrepancy between forward and backward costate
rollouts, which are computationally cheap. We show that the discontinuity of
costate dynamics (in the presence of state constraints) effectively enables the
learning of discontinuous values, without requiring manually supervised data as
suggested by the current SOTA. More importantly, we show that the close
relationship between costates and policies makes the former critical in
learning feedback control policies with generalizable safety performance.

通过引入在前向和后向态演化之间的差异上定义的共态损失，该论文提出了一种 Pontryagin 模式神经运算符，用于处理具有参数状态约束的游戏，该方法在安全性能方面优于现有技术，且无需手动监督数据。

用 Pontryagin 神经算子解决参数化广义和微分博弈

Pontryagin Neural Operator for Solving Parametric General-Sum  Differential Games

This work uses game theory as a mathematical framework to address interaction
modeling in multi-agent motion forecasting and control. Despite its
interpretability, applying game theory to real-world robotics, like automated
driving, faces challenges such as unknown game parameters. To tackle these, we
establish a connection between differential games, optimal control, and
energy-based models, demonstrating how existing approaches can be unified under
our proposed Energy-based Potential Game formulation. Building upon this, we
introduce 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 analysis provides empirical evidence
that the game-theoretic layer adds interpretability and improves the predictive
performance of various neural network backbones using two simulations and two
real-world driving datasets.

利用博弈论作为数学框架，解决多智能体运动预测与控制中的交互建模问题。通过建立微分博弈、最优控制和基于能量的模型之间的联系，提出了基于能量的潜力博弈的统一方法，并介绍了结合神经网络进行博弈参数推断的端到端学习应用，该应用具有可解释性并通过两个模拟实验和两个真实驾驶数据集证明了其对各种神经网络模型的预测性能的改善。

基于能源的潜力博弈用于联合运动预测与控制

Energy-based Potential Games for Joint Motion Forecasting and Control

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.

该研究论文提出了一种基于能量的潜在博弈模型，通过整合神经网络和可微分博弈论优化层，应用于机器人交互中，显示了改进神经网络预测性能的实证结果。

关于多智体互动的微分博弈、最优控制和能量模型之间的关联

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

Mean Field Game systems describe equilibrium configurations in differential
games with infinitely many infinitesimal interacting agents. We introduce a
learning procedure (similar to the Fictitious Play) for these games and show
its convergence when the Mean Field Game is potential.

本文介绍了一种类似于虚构判断游戏的学习过程用于求解 Mean Field Game 系统，并证明了该方法在 Mean Field Game 系统为 potential 时的收敛性。