Flow-based Distributionally Robust Optimization

Published: 07 Nov 2023, Last Modified: 13 Dec 2023M3L 2023 PosterEveryoneRevisionsBibTeX
Keywords: flow-based neural network, distributional robust optimization, worst-case distribution
TL;DR: We develop a flow-based model to solve for the worst-case distribution in high-dimensional distributional robust optimization.
Abstract: Flow-based models establish a continuous-time invertible transport map between a data distribution and a pre-specified target distribution, such as the standard Gaussian in normalizing flow. In this work, we study beyond the constraint of known target distributions. We specifically aim to find the worst-case distribution in distributional robust optimization (DRO), which is an infinite-dimensional problem that becomes particularly challenging in high-dimensional settings. To this end, we introduce a computational tool called FlowDRO Specifically, we reformulate the difficult task of identifying the worst-case distribution within a Wasserstein-2 uncertainty set into a more manageable form, i.e., training parameters of a corresponding flow-based neural network. Notably, the proposed FlowDRO is applicable to general risk functions and data distributions in DRO. We demonstrate the effectiveness of the proposed approach in various high-dimensional problems that can be viewed as DRO, including adversarial attack and differential privacy.
Submission Number: 36