We present a computationally efficient framework, called \texttt{FlowDRO},
for solving flow-based distributionally robust optimization (DRO) problems with
Wasserstein uncertainty sets, when requiring the worst-case distribution (also
called the Least Favorable Distribution, LFD) to be continuous so that the
algorithm can be scalable to problems with larger sample sizes and achieve
better generalization capability for the induced robust algorithms. To tackle
the computationally challenging infinitely dimensional optimization problem, we
leverage flow-based models, continuous-time invertible transport maps between
the data distribution and the target distribution, and develop a Wasserstein
proximal gradient flow type of algorithm. In practice, we parameterize the
transport maps by a sequence of neural networks progressively trained in blocks
by gradient descent. Our computational framework is general, can handle
high-dimensional data with large sample sizes, and can be useful for various
applications. We demonstrate its usage in adversarial learning,
distributionally robust hypothesis testing, and a new mechanism for data-driven
distribution perturbation differential privacy, where the proposed method gives
strong empirical performance on real high-dimensional data.

我们提出了一种计算效率高的框架，称为 FlowDRO，用于解决基于流的分布鲁棒优化（DRO）问题，该框架利用 Wasserstein 不确定性集，并要求最差情况分布（也称为最不利分布，LFD）连续，从而使该算法能够在具有更大样本量的问题中进行扩展，并为引入的鲁棒算法提供更好的泛化能力。