Sinkhorn Distributionally Robust Optimization
This work addresses robust optimization under distributional uncertainty for applications in machine learning and operations research, representing an incremental improvement with a focus on computational efficiency.
The paper tackles distributionally robust optimization using Sinkhorn distance by deriving a convex dual reformulation and developing a stochastic mirror descent algorithm with computational guarantees, demonstrating superior performance in numerical examples.
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.