Meta Optimal Transport

Brandon Amos, Samuel Cohen, Giulia Luise, Ievgen Redko

Keywords: optimal transport, meta learning, amortized optimization

TL;DR: We predict optimal solutions to optimal transport problems given the input measures

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. Meta OT models surpass the standard convergence rates of log-Sinkhorn solvers in the discrete setting and convex potentials in the continuous setting. We improve the computational time of standard OT solvers by multiple orders of magnitude in discrete and continuous transport settings between images, spherical data, and color palettes.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2206.05262/code)