We present an inverse dynamic game-based algorithm to learn parametric constraints from a given dataset of local Nash equilibrium interactions between multiple agents. Specifically, we introduce mixed-integer linear programs (MILP) encoding the Karush-Kuhn-Tucker (KKT) conditions of the interacting agents, which recover constraints consistent with the local Nash stationarity of the interaction demonstrations. We establish theoretical guarantees that our method learns inner approximations of the true safe and unsafe sets. We also use the interaction constraints recovered by our method to design motion plans that robustly satisfy the underlying constraints. Across simulations and hardware experiments, our methods accurately inferred constraints and designed safe interactive motion plans for various classes of constraints, both convex and non-convex, from interaction demonstrations of agents with nonlinear dynamics.

翻译：我们提出一种基于逆动态博弈的算法，用于从给定的多智能体局部纳什均衡交互数据集中学习参数化约束。具体而言，我们引入了编码交互智能体卡鲁什-库恩-塔克（KKT）条件的混合整数线性规划（MILP），该规划能够恢复与交互演示的局部纳什平稳性相一致的约束。我们建立了理论保证，证明我们的方法能够学习真实安全集与非安全集的内近似。此外，我们利用本方法恢复的交互约束来设计鲁棒满足底层约束的运动规划。在仿真与硬件实验中，我们的方法从具有非线性动力学的智能体交互演示中，针对凸与非凸的各类约束，均能准确推断约束并设计安全的交互运动规划。