Optimal transport divergences induced by scoring functions

Silvana M. Pesenti; Steven Vanduffel

doi:10.1016/j.orl.2024.107146

Optimal transport divergences induced by scoring functions

Silvana M. Pesenti, Steven Vanduffel

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives rise to a rich variety of novel asymmetric MK divergences, subsuming Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. We conclude with two applications to robust optimisation.

Original language	English
Article number	107146
Pages (from-to)	1-8
Number of pages	8
Journal	Operations research letters
Volume	57
DOIs	https://doi.org/10.1016/j.orl.2024.107146
Publication status	Published - Nov 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

Keywords

Asymmetric optimal transport
Elicitability
Optimal transport
Risk measures
Scoring functions
Wasserstein distance

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abstract = "We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives rise to a rich variety of novel asymmetric MK divergences, subsuming Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. We conclude with two applications to robust optimisation.",

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AU - Vanduffel, Steven

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AB - We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives rise to a rich variety of novel asymmetric MK divergences, subsuming Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. We conclude with two applications to robust optimisation.

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KW - Elicitability

KW - Optimal transport

KW - Risk measures

KW - Scoring functions

KW - Wasserstein distance

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JF - Operations research letters

M1 - 107146

ER -

Optimal transport divergences induced by scoring functions

Abstract

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Keywords

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