Stochastic Optimal Control via Local Occupation Measures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916569556189184 |
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| author | Holtorf, Flemming Edelman, Alan Rackauckas, Christopher |
| author_facet | Holtorf, Flemming Edelman, Alan Rackauckas, Christopher |
| contents | Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the traditional occupation measure framework derived from resolving the occupation measures locally on a partition of the control problem's space-time domain. This notion of local occupation measures provides fine-grained control over the construction of structured semidefinite programming relaxations for a rich class of stochastic optimal control problems with embedded diffusion and jump processes via the moment-sum-of-squares hierarchy. As such, it bridges the gap between discretization-based approximations to the Hamilton-Jacobi-Bellmann equations and occupation measure relaxations. We demonstrate with examples that this approach enables the computation of high quality bounds for the optimal value of a large class of stochastic optimal control problems with significant performance gains relative to the traditional occupation measure framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15652 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimal Control via Local Occupation Measures Holtorf, Flemming Edelman, Alan Rackauckas, Christopher Optimization and Control Systems and Control Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the traditional occupation measure framework derived from resolving the occupation measures locally on a partition of the control problem's space-time domain. This notion of local occupation measures provides fine-grained control over the construction of structured semidefinite programming relaxations for a rich class of stochastic optimal control problems with embedded diffusion and jump processes via the moment-sum-of-squares hierarchy. As such, it bridges the gap between discretization-based approximations to the Hamilton-Jacobi-Bellmann equations and occupation measure relaxations. We demonstrate with examples that this approach enables the computation of high quality bounds for the optimal value of a large class of stochastic optimal control problems with significant performance gains relative to the traditional occupation measure framework. |
| title | Stochastic Optimal Control via Local Occupation Measures |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2211.15652 |