Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes
研究了具有局部强凸传输代价函数和仿射决策规则的最优传输分布鲁棒优化问题，揭示了其结构性质，并据此设计了与非鲁棒基准算法复杂度相同的有效优化程序。
We consider optimal transport-based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded in the DRO problem (e.g., strong convexity even if the non-DRO problem is not strongly convex, a suitable scaling of the Lagrangian for the DRO constraint, etc., which are crucial for the design of efficient algorithms). As a consequence of these results, one can develop efficient optimization procedures that have the same sample and iteration complexity as a natural non-DRO benchmark algorithm, such as stochastic gradient descent.