Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze stochastic algorithms that apply to both non-convex and convex losses for solving Kullback Leibler divergence constrained DRO problem. Compared with existing methods solving this problem, our stochastic algorithms not only enjoy competitive if not better complexity independent of sample size but also just require a constant batch size at every iteration, which is more practical for broad applications. We establish a nearly optimal complexity bound for finding an $\epsilon$ stationary solution for non-convex losses and an optimal complexity for finding an $\epsilon$ optimal solution for convex losses. Empirical studies demonstrate the effectiveness of the proposed algorithms for solving non-convex and convex constrained DRO problems.

本文提出并分析了一种基于随机算法的方法，用于解决Kullback Leibler divergence约束的Distributionally Robust Optimization问题，该方法适用于非凸和凸损失函数，并具有更高的竞争性和更实用的常数批量大小迭代复杂度。

具有样本大小无关性的随机约束 DRO