Meta Optimal Transport

Brandon Amos, Giulia Luise, Samuel Cohen, Ievgen Redko
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:791-813, 2023.

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

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-amos23a, title = {Meta Optimal Transport}, author = {Amos, Brandon and Luise, Giulia and Cohen, Samuel and Redko, Ievgen}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {791--813}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/amos23a/amos23a.pdf}, url = {https://proceedings.mlr.press/v202/amos23a.html}, 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} }
Endnote
%0 Conference Paper %T Meta Optimal Transport %A Brandon Amos %A Giulia Luise %A Samuel Cohen %A Ievgen Redko %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-amos23a %I PMLR %P 791--813 %U https://proceedings.mlr.press/v202/amos23a.html %V 202 %X 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
APA
Amos, B., Luise, G., Cohen, S. & Redko, I.. (2023). Meta Optimal Transport. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:791-813 Available from https://proceedings.mlr.press/v202/amos23a.html.

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