Abstract: We study Sinkhorn contextual robust optimization, where a decision-maker learns a context-dependent policy under a Sinkhorn-penalized worst-case objective over joint context-outcome distributions. The resulting minimax problem is infinite-dimensional in both the policy and distribution spaces. Existing approaches often optimize a parameterized policy, but this can obscure global convergence guarantees and make feasibility constraints difficult to enforce, even when each per-context decision problem is convex. We instead interchange the minimax order, obtaining a max-min formulation in which the inner policy problem decomposes across contexts and can be solved in parallel using optimization tools tailored to the original decision space and constraints, while the outer maximization identifies a least-favorable distribution. To solve this outer problem, we reparameterize adversarial distributions by a family of conditional distributions that map empirical samples to perturbed ones, and derive a Langevin ascent scheme for the reparameterized problem from a gradient-flow perspective. We establish global convergence of the resulting discrete-time dynamics and provide performance guarantees for the policy induced from the learned distribution. Computationally, we represent the conditional distributions by Gaussian mixtures, yielding an efficient gradient estimation. Numerical experiments show improved optimality and feasibility over standard policy-parameterization approaches.

Bio: Rui Gao is an Associate Professor in the Department of Information, Risk, and Operations Management at McCombs School of Business at The University of Texas at Austin. His primary research focus is on data-driven decision-making and Artificial Intelligence. He received a Ph.D. in Operations Research from Georgia Institute of Technology, and a B.Sc. in Mathematics and Applied Mathematics from Xi'an Jiaotong University.