We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.

翻译：本文研究基于Sinkhorn距离（一种采用熵正则化的Wasserstein距离变体）的分布鲁棒优化问题。针对一般名义分布、传输代价与损失函数，我们推导出凸规划对偶重构形式。为求解该对偶问题，我们提出一种带有偏置次梯度估计器的随机镜像下降算法，并给出其计算复杂度理论保证。最后，通过合成数据与真实数据的数值实验，验证了所提方法的优越性能。