Splitting Algorithms for Distributionally Robust Optimization

TL;DR

This paper introduces novel splitting algorithms for distributionally robust optimization with discrete uncertainties, focusing on proximity operators and monotone inclusions, and demonstrates their effectiveness on inverse and denoising problems.

Contribution

It proposes new splitting methods based on proximity operators and monotone inclusions for robust optimization problems with discrete uncertainties.

Findings

Algorithms efficiently solve inverse problems under uncertainty.

Numerical results show improved convergence and performance.

Methods are applicable to denoising with uncertain data.

Abstract

In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity operator of the supremum function that appears in the optimization problem. The second method solves an equivalent monotone inclusion formulation derived from the first-order optimality conditions, where the resolvents of the monotone operators involved in the inclusion are computable. The proposed methods are applied to solve the Couette inverse problem with uncertainty and the denoising problem with uncertainty. We present numerical results to compare the efficiency of the algorithms.