Distributionally Robust Optimization via Diffusion Ambiguity Modeling

2025-10-26

AI Summary

Distributionally robust optimization (DRO) faces a fundamental trade-off in ambiguity set design: ensuring fidelity to the nominal distribution while accommodating scenario diversity and preserving computational tractability. Method: We propose diffusion-driven DRO (D-DRO), the first framework to integrate diffusion models into ambiguity set construction. By parameterizing the diffusion process, D-DRO generates a rich, structurally expressive family of adversarial distributions with flexible support—overcoming expressivity limitations inherent in conventional moment- or φ-divergence-based ambiguity sets. Contribution/Results: We establish theoretical guarantees on the stationary convergence of D-DRO solutions. Empirically, D-DRO consistently improves out-of-distribution generalization across diverse machine learning prediction tasks—including regression, classification, and time-series forecasting—while retaining computational efficiency and scalability. The framework bridges statistical robustness, generative modeling, and optimization, offering a principled, expressive, and tractable approach to distributional uncertainty quantification.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationMachine Learning: Adversarial Learning & RobustnessComputer Vision: Diffusion Models for Vision

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Designing diffusion-based ambiguity sets for robust optimization
• Solving tractable DRO with parameterized diffusion model space
• Enhancing OOD generalization in machine learning tasks

Innovation

• Diffusion-based ambiguity set for diverse adversarial distributions
• Tractable D-DRO algorithm with parameterized diffusion model space
• Ensures stationary convergence and OOD generalization performance