Online Control of Linear Systems under Unbounded Noise
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912406728343552 |
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| author | Ito, Kaito Tsuchiya, Taira |
| author_facet | Ito, Kaito Tsuchiya, Taira |
| contents | This paper investigates the problem of controlling a linear system under possibly unbounded stochastic noise with unknown convex cost functions, known as an online control problem. In contrast to the existing work, which assumes the boundedness of noise, we show that an $ \tilde{O}(\sqrt{T}) $ high-probability regret can be achieved under unbounded noise, where $ T $ denotes the time horizon. Notably, the noise is only required to have a finite fourth moment. Moreover, when the costs are strongly convex and the noise is sub-Gaussian, we establish an $ O({\rm poly} (\log T)) $ regret bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Online Control of Linear Systems under Unbounded Noise Ito, Kaito Tsuchiya, Taira Systems and Control Machine Learning Optimization and Control This paper investigates the problem of controlling a linear system under possibly unbounded stochastic noise with unknown convex cost functions, known as an online control problem. In contrast to the existing work, which assumes the boundedness of noise, we show that an $ \tilde{O}(\sqrt{T}) $ high-probability regret can be achieved under unbounded noise, where $ T $ denotes the time horizon. Notably, the noise is only required to have a finite fourth moment. Moreover, when the costs are strongly convex and the noise is sub-Gaussian, we establish an $ O({\rm poly} (\log T)) $ regret bound. |
| title | Online Control of Linear Systems under Unbounded Noise |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2402.10252 |