Department of Industrial Engineering & Decision Analytics [Joint IEDA/ISOM seminar] - Optimal Transport for Matching and Simulation

Optimal transport provides a powerful mathematical framework for comparing probability distributions, with applications ranging from matching structured data to simulation and decision-making under uncertainty. In this talk, I will discuss two recent works that explore how optimal transport can be used to address two distinct challenges in optimization and machine learning. In the first part, I consider the Gromov–Wasserstein (GW) problem, which seeks to match objects across incomparable spaces by preserving their underlying geometric structures. Since GW is formulated as a nonconvex quadratic optimization problem, existing algorithms typically provide only locally optimal solutions. I will present a semidefinite programming relaxation that provides computable lower bounds and, in many instances, certifies global optimality. I will also discuss its applications to graph and shape matching. In the second part, I turn to conditional distribution learning, motivated by simulation and personalized decision-making. When observations are scarce, accurately estimating an entire conditional distribution can be substantially more challenging than predicting its mean. I will introduce GENTLE, a neural generative model that combines distributional fitting with entropic optimal transport regularization to learn conditional distributions from limited data. Numerical experiments demonstrate its effectiveness in recovering conditional distributions on real-world and simulation datasets. Together, these works illustrate how optimal transport connects convex optimization, generative modeling, and data-driven decision-making.