Randomized Transport Plans via Hierarchical Fully Probabilistic Design
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913824685162496 |
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| author | Y., Sarah Boufelja Quinn, Anthony Shorten, Robert |
| author_facet | Y., Sarah Boufelja Quinn, Anthony Shorten, Robert |
| contents | An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in fair market matching is outlined, in which HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_02701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomized Transport Plans via Hierarchical Fully Probabilistic Design Y., Sarah Boufelja Quinn, Anthony Shorten, Robert Systems and Control Optimization and Control Machine Learning An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in fair market matching is outlined, in which HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan. |
| title | Randomized Transport Plans via Hierarchical Fully Probabilistic Design |
| topic | Systems and Control Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2408.02701 |