Sinkhorn Distributionally Robust Optimization

We study distributionally robust optimization with Sinkorn distance---a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulations when the nominal distribution is an empirical distribution and a general distribution, respectively. Compared with Wasserstein DRO, it is computationally tractable for a larger class of loss functions, and its worst-case distribution is more reasonable. To solve the dual reformulation, we propose an efficient batch gradient descent with bisection search algorithm. Finally, we provide various numerical examples using both synthetic and real data to demonstrate its competitive performance.

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