Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Geometry, large deviation and Selection Principles in Entropic Optimal Transport
Speaker: Promit Ghosal
Date: September 10, 2025
Time: 14:30:00 Hours
Venue: A-369
Abstract: Entropically regularized optimal transport (EOT) has emerged as a powerful computational and theoretical tool in mathematics, statistics and machine learning, yet its small-regularization limit remains subtle, especially in dimensions d>1. In this talk, I will present recent progress on understanding the convergence of EOT to optimal transport in the vanishing regularization regime. Building on ideas from optimal transport geometry and large deviations theory, we quantify the local exponential convergence of entropic optimizers and characterize the exact rate function in terms of the Kantorovich potential. I will then focus on a new selection principle for the Monge transport plan when the cost is the Euclidean distance, and the marginals are absolutely continuous. We show that the limiting plan is supported on transport rays and is uniquely determined within each ray by minimizing a relative entropy functional with respect to a canonical reference measure. This variational characterization provides a complete and unique description of the limiting transport plan.
Title of Talk: Geometry, large deviation and Selection Principles in Entropic Optimal Transport
Speaker: Promit Ghosal
Date: September 10, 2025
Time: 14:30:00 Hours
Venue: A-369
Abstract: Entropically regularized optimal transport (EOT) has emerged as a powerful computational and theoretical tool in mathematics, statistics and machine learning, yet its small-regularization limit remains subtle, especially in dimensions d>1. In this talk, I will present recent progress on understanding the convergence of EOT to optimal transport in the vanishing regularization regime. Building on ideas from optimal transport geometry and large deviations theory, we quantify the local exponential convergence of entropic optimizers and characterize the exact rate function in terms of the Kantorovich potential. I will then focus on a new selection principle for the Monge transport plan when the cost is the Euclidean distance, and the marginals are absolutely continuous. We show that the limiting plan is supported on transport rays and is uniquely determined within each ray by minimizing a relative entropy functional with respect to a canonical reference measure. This variational characterization provides a complete and unique description of the limiting transport plan.