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Stability of entropic optimal transport and Schrödinger bridges.

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Title: Stability of entropic optimal transport and Schrödinger bridges.
Authors: Ghosal, Promit1 (AUTHOR) promit@mit.edu, Nutz, Marcel1,2 (AUTHOR) mnutz@columbia.edu, Bernton, Espen3 (AUTHOR) eb3311@columbia.edu
Source: Journal of Functional Analysis. Nov2022, Vol. 283 Issue 9, pN.PAG-N.PAG. 1p.
Subjects: Cost functions
Abstract: We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the use of c -cyclical monotonicity in classical optimal transport. As a consequence of stability, we obtain the wellposedness of the solution in this geometric sense, even when all transports have infinite cost. More generally, our results apply to a class of static Schrödinger bridge problems including entropic optimal transport. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: Stability of entropic optimal transport and Schrödinger bridges.
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  Data: <searchLink fieldCode="AR" term="%22Ghosal%2C+Promit%22">Ghosal, Promit</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> promit@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Nutz%2C+Marcel%22">Nutz, Marcel</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> mnutz@columbia.edu</i><br /><searchLink fieldCode="AR" term="%22Bernton%2C+Espen%22">Bernton, Espen</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> eb3311@columbia.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Nov2022, Vol. 283 Issue 9, pN.PAG-N.PAG. 1p.
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  Data: We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the use of c -cyclical monotonicity in classical optimal transport. As a consequence of stability, we obtain the wellposedness of the solution in this geometric sense, even when all transports have infinite cost. More generally, our results apply to a class of static Schrödinger bridge problems including entropic optimal transport. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.jfa.2022.109622
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      – Code: eng
        Text: English
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      – SubjectFull: Cost functions
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      – TitleFull: Stability of entropic optimal transport and Schrödinger bridges.
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            NameFull: Ghosal, Promit
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            NameFull: Nutz, Marcel
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            NameFull: Bernton, Espen
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            – D: 01
              M: 11
              Text: Nov2022
              Type: published
              Y: 2022
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