Drago: Primal-Dual Coupled Variance Reduction for Faster Distributionally Robust Optimization

Ronak Mehta; Jelena Diakonikolas; Zaid Harchaoui

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arXiv · 2403.10763

Drago: Primal-Dual Coupled Variance Reduction for Faster Distributionally Robust Optimization

Ronak Mehta·Jelena Diakonikolas·Zaid Harchaoui

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Abstract

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic primal-dual algorithm that combines cyclic and randomized components with a carefully regularized primal update to achieve dual variance reduction. Owing to its design, Drago enjoys a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems with a fine-grained dependency on primal and dual condition numbers. Theoretical results are supported by numerical benchmarks on regression and classification tasks.

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Ronak Mehta, Jelena Diakonikolas, Zaid Harchaoui. 2024-03-16. Drago: Primal-Dual Coupled Variance Reduction for Faster Distributionally Robust Optimization. https://arxiv.org/abs/2403.10763

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