发表机构
Digital Futures, KTH Royal Institute of Technology（数字未来中心，皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究数据驱动Wasserstein分布鲁棒线性二次控制中，为防范分布模糊所付出的保守性代价，给出了样本复杂度界，证明次优性随Wasserstein半径至多线性（局部）或二次增长，并用数值模拟验证。
AI 中文摘要
分布鲁棒（DR）优化旨在寻找在给定模糊集内最不利分布下表现最佳的决策，从而能够在面对不确定性时设计具有强样本外保证的数据驱动控制器。本文研究了为防范分布模糊而引入的保守性。具体而言，我们考虑数据驱动的Wasserstein分布鲁棒线性二次控制问题，并分析相应解相对于使用底层未知不确定性分布的先验知识计算出的预言控制器而言的次优性。我们给出了一个样本复杂度界，该界刻画了确保DR解的真实成本超过预言控制器的成本至多一个用户定义的容差因子所需的样本数量。我们的分析表明，对于足够小的分布模糊，DR解的次优性随Wasserstein半径至多线性增长，而在远离该局部区域时至多二次增长。数值模拟验证了我们关于分布鲁棒性代价的界。
英文摘要
Distributionally robust (DR) optimization seeks decisions that perform best under the most adverse law within a given ambiguity set, enabling the design of data-driven controllers with strong out-of-sample guarantees in the face of uncertainty. In this paper, we study the conservatism introduced by safeguarding against distributional ambiguity. Specifically, we consider the data-driven Wasserstein DR linear quadratic control problem, and we analyze the suboptimality of the corresponding solution relative to the oracle controller computed with foreknowledge of the underlying unknown uncertainty distribution. We present a sample complexity bound that characterizes the number of samples required to ensure that the true cost of the DR solution exceeds that of the oracle controller by at most a user-defined tolerance factor. Our analysis reveals that the suboptimality of the DR solution increases at most linearly with the Wasserstein radius for sufficiently small distributional ambiguity, and at most quadratically away from this local regime. Numerical simulations validate our bounds on the price of distributional robustness.
