Distributionally Robust Optimization via Diffusion Ambiguity Modeling
This work addresses the problem of enhancing robustness in statistical learning for applications requiring reliable performance under distribution shifts, representing an incremental advancement in DRO methodology.
The paper tackles the challenge of designing effective ambiguity sets for Distributionally Robust Optimization (DRO) to improve robustness and generalization, proposing a diffusion-based ambiguity set and D-DRO algorithm that achieves superior Out-of-Distribution generalization performance in a machine learning prediction task.
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.