Meta Optimal Transport

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Volume Title
Conference article
Date
2023
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Mcode
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Language
en
Pages
23
791-813
Series
Proceedings of Machine Learning Research, Volume 202
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 sub-optimally 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.
Description
Funding Information: We would like to thank Eugene Vinitsky, Mark Tygert, Mathieu Blondel, Maximilian Nickel, and Muhammad Izzatullah for insightful comments and discussions. The core set of tools in Python (Van Rossum and Drake Jr, 1995; Oliphant, 2007) enabled this work, including Hydra (Yadan, 2019), JAX (Bradbury et al., 2018), Matplotlib (Hunter, 2007), numpy (Oliphant, 2006; Van Der Walt et al., 2011), Optimal Transport Tools (Cuturi et al., 2022), and pandas (McKinney, 2012). Publisher Copyright: © 2023 Proceedings of Machine Learning Research. All rights reserved.
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Citation
Amos , B , Luise , G , Cohen , S & Redko , I 2023 , ' Meta Optimal Transport ' , Proceedings of Machine Learning Research , vol. 202 , pp. 791-813 . < https://proceedings.mlr.press/v202/amos23a.html >