Optimal control under unknown intensity with Bayesian learning
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915688944238592 |
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| author | Baradel, Nicolas Cormier, Quentin |
| author_facet | Baradel, Nicolas Cormier, Quentin |
| contents | We investigate an optimal control problem motivated by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an unknown parameter. Given a prior distribution for the unknown parameter, we describe its evolution using Bayes' rule. We reformulate the optimization problem by applying Girsanov's theorem and establish a dynamic programming principle. Finally, we characterize the value function as the unique viscosity solution to a finite-dimensional Hamilton-Jacobi-Bellman equation, which can be solved numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control under unknown intensity with Bayesian learning Baradel, Nicolas Cormier, Quentin Optimization and Control Probability 62M20, 49L20, 49L25 We investigate an optimal control problem motivated by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an unknown parameter. Given a prior distribution for the unknown parameter, we describe its evolution using Bayes' rule. We reformulate the optimization problem by applying Girsanov's theorem and establish a dynamic programming principle. Finally, we characterize the value function as the unique viscosity solution to a finite-dimensional Hamilton-Jacobi-Bellman equation, which can be solved numerically. |
| title | Optimal control under unknown intensity with Bayesian learning |
| topic | Optimization and Control Probability 62M20, 49L20, 49L25 |
| url | https://arxiv.org/abs/2411.04917 |