Stochastic Constrained DRO with a Complexity Independent of Sample Size

• URL: http://arxiv.org/abs/2210.05740v2
• Date: Wed, 16 Aug 2023 07:06:58 GMT
• Title: Stochastic Constrained DRO with a Complexity Independent of Sample Size
• Authors: Qi Qi, Jiameng Lyu, Kung sik Chan, Er Wei Bai, Tianbao Yang
• Abstract summary: We propose and analyze algorithms that apply to both non- and convex losses for solving Kullback divergence constrained DRO problem. We establish a nearly optimal complexity for finding an $$ilon stationary solution for non- losses and an optimal batch complexity for finding an optimal solution for broad applications.
• Score: 38.56406595022129
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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