Dynamic Programming in Probability Spaces via Optimal Transport
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909162510745600 |
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| author | Terpin, Antonio Lanzetti, Nicolas Dörfler, Florian |
| author_facet | Terpin, Antonio Lanzetti, Nicolas Dörfler, Florian |
| contents | We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the "ground space" (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: The "low-level control of the agents of the fleet" (how does one reach the destination?) and "fleet-level control" (who goes where?) are decoupled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamic Programming in Probability Spaces via Optimal Transport Terpin, Antonio Lanzetti, Nicolas Dörfler, Florian Optimization and Control Systems and Control We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the "ground space" (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: The "low-level control of the agents of the fleet" (how does one reach the destination?) and "fleet-level control" (who goes where?) are decoupled. |
| title | Dynamic Programming in Probability Spaces via Optimal Transport |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2302.13550 |