逆线性二次高斯博弈：约束设置与可迁移性
Inverse Linear Quadratic Gaussian Games: Constrained Setting and Transferability
- École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
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AI总结：
本文研究有限时域逆线性二次高斯博弈，在约束下刻画并计算生成广义纳什均衡的成本参数与对偶值，在无约束下证明成本值扰动随动力学及参数偏差线性增长，并通过仿真和机器人实验验证可迁移性。
AI中文摘要：
本工作研究有限时域逆线性二次高斯博弈。在约束设置下，我们刻画了生成给定广义纳什均衡的成本参数和最优对偶值的集合，并提出一种算法来计算这些参数。在无约束设置下，我们处理可迁移性问题，即在一组不同动力学条件下，界定由识别出的成本参数所诱导的策略与由专家参数所诱导的策略之间的成本值扰动。该成本值扰动随动力学偏差和识别出的成本参数偏差线性增长。通过数值模拟，我们表明在约束设置下，我们的算法能够识别出可复现与观测到的广义纳什均衡相对应的策略和轨迹的成本参数和对偶值。在无约束设置下，我们通过交通仿真和真实机器人实验表明，识别出的成本参数可用于控制足够接近的动力学，其性能随动力学偏差和识别出的成本参数偏差线性下降。
英文摘要：
This work addresses finite-horizon inverse linear quadratic Gaussian games. In a constrained setting, we characterize the set of cost parameters and optimal dual values that generate a given generalized Nash equilibrium, and we propose an algorithm to compute these parameters. In an unconstrained setting, we address transferability, namely, we bound the cost value perturbation between two policies: one induced by the identified cost parameters, the other by the expert parameters, under a set of different dynamics. This cost value perturbation scales linearly with the deviations in the dynamics and the identified cost parameters. Through numerical simulations, we show that, in a constrained setting, our algorithm identifies the cost parameters and dual values that can reproduce the policy and trajectories corresponding to the observed generalized Nash equilibrium. In an unconstrained setting, we show with a traffic simulation and real-robot experiments that the identified cost parameters can be used to control sufficiently close dynamics, with performance degrading linearly with the deviations in the dynamics and the identified cost parameters.
