The Pontryagin maximum principle and $Q$-functions in rough environments
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917191371194368 |
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| author | Ashkarian, Estepan Chakraborty, Prakash Honnappa, Harsha Tindel, Samy |
| author_facet | Ashkarian, Estepan Chakraborty, Prakash Honnappa, Harsha Tindel, Samy |
| contents | We derive the Pontryagin maximum principle and $Q$-functions for the relaxed control of noisy rough differential equations. Our main tool is the development of a novel differentiation procedure along `spike variation' perturbations of the optimal state-control pair. We then exploit our development of the infinitesimal $Q$-function (also known as the $q$-function) to derive a policy improvement algorithm for settings with entropic cost constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Pontryagin maximum principle and $Q$-functions in rough environments Ashkarian, Estepan Chakraborty, Prakash Honnappa, Harsha Tindel, Samy Optimization and Control Probability We derive the Pontryagin maximum principle and $Q$-functions for the relaxed control of noisy rough differential equations. Our main tool is the development of a novel differentiation procedure along `spike variation' perturbations of the optimal state-control pair. We then exploit our development of the infinitesimal $Q$-function (also known as the $q$-function) to derive a policy improvement algorithm for settings with entropic cost constraints. |
| title | The Pontryagin maximum principle and $Q$-functions in rough environments |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2601.05354 |