Distributionally Robust Optimization via Diffusion Ambiguity Modeling

TL;DR

This paper introduces a diffusion-based ambiguity set for Distributionally Robust Optimization, enabling more flexible and tractable solutions that improve out-of-distribution generalization in machine learning tasks.

Contribution

It proposes a novel diffusion-based ambiguity set for DRO and develops D-DRO, a tractable algorithm with proven convergence and enhanced OOD performance.

Findings

D-DRO achieves superior OOD generalization.

The ambiguity set captures diverse adversarial distributions.

The method is theoretically proven to converge.

Abstract

This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions that remain consistent with the nominal distribution while being diverse enough to account for a variety of potential scenarios. Moreover, it should lead to tractable DRO solutions. To this end, we propose a diffusion-based ambiguity set design that captures various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this ambiguity modeling, we propose Diffusion-based DRO (D-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized diffusion model space. We formally establish the stationary convergence performance of D-DRO and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in a ML prediction task.