Meta Optimal Transport

Brandon Amos, Samuel Cohen, Giulia Luise, Ievgen Redko

Keywords: optimal transport, meta learning, amortized optimization

TL;DR: We learn to predict the solution to optimal transport problems

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 (Wasserstein-2) settings between images, spherical data, and color palettes and use them to improve the computational time of standard OT solvers by multiple orders of magnitude.

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Please Choose The Closest Area That Your Submission Falls Into: Optimization (eg, convex and non-convex optimization)

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