Semidiscrete optimal transport with unknown costs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915741708582912 |
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| author | Zhu, Yinchu Ryzhov, Ilya O. |
| author_facet | Zhu, Yinchu Ryzhov, Ilya O. |
| contents | Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed marginals, in a way that minimizes expected cost. We formulate a novel variant of this problem in which the cost functions are unknown, but can be learned through noisy observations; however, only one function can be sampled at a time. We develop a semi-myopic algorithm that couples online learning with stochastic approximation, and prove that it achieves optimal convergence rates, despite the non-smoothness of the stochastic gradient and the lack of strong concavity in the objective function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00786 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semidiscrete optimal transport with unknown costs Zhu, Yinchu Ryzhov, Ilya O. Econometrics Statistics Theory Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed marginals, in a way that minimizes expected cost. We formulate a novel variant of this problem in which the cost functions are unknown, but can be learned through noisy observations; however, only one function can be sampled at a time. We develop a semi-myopic algorithm that couples online learning with stochastic approximation, and prove that it achieves optimal convergence rates, despite the non-smoothness of the stochastic gradient and the lack of strong concavity in the objective function. |
| title | Semidiscrete optimal transport with unknown costs |
| topic | Econometrics Statistics Theory |
| url | https://arxiv.org/abs/2310.00786 |