发表机构
École Polytechnique Fédérale de Lausanne (EPFL); ETH Zürich（洛桑联邦理工学院; 苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间相关扰动的分布鲁棒线性二次控制，证明最优策略为仿射且最坏分布为标称分布的仿射推前，并提出高效算法，实验验证了样本外性能优势。
AI 中文摘要
我们研究了有限时域分布鲁棒线性二次控制问题，其中扰动在时间上可以任意相关。模糊集被建模为一个以扰动的标称椭圆等高分布为中心的单一2-Wasserstein球。尽管策略空间和模糊集都是无限维的，我们证明了最优策略是仿射的，且最坏情况分布是标称分布的仿射推前。这些仿射映射可以通过基于Frank--Wolfe算法的最佳响应算法高效计算。实验表明，当真实扰动相关时，所提方法相比LQG及其分布鲁棒扩展具有更好的样本外性能，而在扰动不相关时仅损失少量性能。
英文摘要
We study finite-horizon distributionally robust linear-quadratic control with disturbances that can be arbitrarily correlated in time. The ambiguity set is modeled as a single 2-Wasserstein ball centered at a nominal elliptically contoured distribution of the disturbances. Despite the infinite-dimensionality of both the policy space and ambiguity set, we prove that the optimal policy is affine and that the worst-case distribution is an affine push-forward of the nominal distribution. These affine maps can be computed efficiently via a best-response algorithm based on the Frank--Wolfe algorithm. Experiments demonstrate improved out-of-sample performance over LQG and its distributionally robust extensions when the true disturbances are correlated, incurring only a small loss of performance under uncorrelated disturbances.
CommentsAccepted to the IEEE Conference on Decision and Control (CDC) 2026
