Flow-Based High-Dimensionally Distributional Robust Optimization

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.