Meta Optimal Transport

TL;DR

Meta OT introduces an amortized optimization approach to predict optimal transport maps efficiently across similar problems, significantly reducing computation time by leveraging past solutions in various data settings.

Contribution

It presents a novel Meta OT framework that uses amortized optimization to improve the efficiency of solving multiple related optimal transport problems.

Findings

Reduces computational time of OT solvers

Applies to diverse data types like images and labels

Demonstrates effectiveness in discrete and continuous settings

Abstract

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot