Meta Optimal Transport

Brandon Amos; Giulia Luise; Samuel Cohen; Ievgen Redko

Meta Optimal Transport

Brandon Amos^*
, Giulia Luise
, Samuel Cohen
, Ievgen Redko

^*Corresponding author for this work

Microsoft USA
University College London
Meta AI Research
Fairgen
Huawei

Research output: Contribution to journal › Conference article › Scientific › peer-review

6 Citations (Scopus)

126 Downloads (Pure)

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.

Original language	English
Pages (from-to)	791-813
Number of pages	23
Journal	Proceedings of Machine Learning Research
Volume	202
Publication status	Published - 2023
MoE publication type	A4 Conference publication
Event	International Conference on Machine Learning - Honolulu, United States Duration: 23 Jul 2023 → 29 Jul 2023 Conference number: 40

Funding

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).

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amos23aFinal published version, 9.67 MBLicence: CC BY

https://proceedings.mlr.press/v202/amos23a.html

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title = "Meta Optimal Transport",

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.",

author = "Brandon Amos and Giulia Luise and Samuel Cohen and Ievgen Redko",

note = "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: {\textcopyright} 2023 Proceedings of Machine Learning Research. All rights reserved.; International Conference on Machine Learning, ICML ; Conference date: 23-07-2023 Through 29-07-2023",

year = "2023",

language = "English",

volume = "202",

pages = "791--813",

journal = "Proceedings of Machine Learning Research",

issn = "2640-3498",

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}

TY - JOUR

T1 - Meta Optimal Transport

AU - Amos, Brandon

AU - Luise, Giulia

AU - Cohen, Samuel

AU - Redko, Ievgen

N1 - Conference code: 40

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85174402709

M3 - Conference article

AN - SCOPUS:85174402709

SN - 2640-3498

VL - 202

SP - 791

EP - 813

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - International Conference on Machine Learning

Y2 - 23 July 2023 through 29 July 2023

ER -

Meta Optimal Transport

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