A Vector Bernstein Inequality for Self-Normalized Martingales
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915090179031040 |
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| author | Ziemann, Ingvar |
| author_facet | Ziemann, Ingvar |
| contents | We prove a Bernstein inequality for vector-valued self-normalized martingales. We first give an alternative perspective of the corresponding sub-Gaussian bound due to Abbasi-Yadkori et al. via a PAC-Bayesian argument with Gaussian priors. By instantiating this argument to priors drawn uniformly over well-chosen ellipsoids, we obtain a Bernstein bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Vector Bernstein Inequality for Self-Normalized Martingales Ziemann, Ingvar Probability We prove a Bernstein inequality for vector-valued self-normalized martingales. We first give an alternative perspective of the corresponding sub-Gaussian bound due to Abbasi-Yadkori et al. via a PAC-Bayesian argument with Gaussian priors. By instantiating this argument to priors drawn uniformly over well-chosen ellipsoids, we obtain a Bernstein bound. |
| title | A Vector Bernstein Inequality for Self-Normalized Martingales |
| topic | Probability |
| url | https://arxiv.org/abs/2412.20949 |