WASSERSTEIN DISTRIBUTIONALLY ROBUST NONPARAMETRIC REGRESSION

发布时间：2026-06-02 作者：浏览次数：

Speaker:	刘常钰	DateTime:	2026年6月15日（周一）上午10:30-11:30
Brief Introduction to Speaker: 刘常钰，武汉大学武汉数学与智能研究院		Place:	国交2号楼315会议室
Abstract:Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worstcase risk within a prescribed ambiguity set. Although WDRO has been extensively studied in parametric settings, its theoretical properties in nonparametric frameworks remain underexplored. This paper investigates WDRO for nonparametric regression. We first establish a structural distinction based on the order k of the Wasserstein distance, showing that k = 1 induces Lipschitz-type regularization, whereas k > 1 corresponds to gradient-norm regularization. To address model misspecification, we analyze the excess local worst-case risk, deriving non-asymptotic error bounds for estimators constructed using norm-constrained feedforward neural networks. This analysis is supported by new covering number and approximation bounds that simultaneously control both the function and its gradient. The proposed estimator achieves a convergence rate of n−2β/...