Distributionally Robust Optimization via Generative Ambiguity Modeling
This work addresses robustness and generalization issues in statistical learning and optimization, offering a novel method for DRO with potential broad impact, though it appears incremental in advancing existing DRO frameworks.
The paper tackles the challenge of designing effective ambiguity sets for Distributionally Robust Optimization (DRO) to improve robustness and generalization, proposing a generative model-based approach that achieves superior Out-of-Distribution generalization performance in ML tasks.
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 to 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 generative model-based ambiguity sets that capture various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this generative ambiguity modeling, we propose DRO with Generative Ambiguity Set (GAS-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized generative model space. We formally establish the stationary convergence performance of GAS-DRO. We implement GAS-DRO with a diffusion model and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in ML tasks.