The Conditional Regret-Capacity Theorem for Batch Universal Prediction
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909736669020160 |
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| author | Bondaschi, Marco Gastpar, Michael |
| author_facet | Bondaschi, Marco Gastpar, Michael |
| contents | We derive a conditional version of the classical regret-capacity theorem. This result can be used in universal prediction to find lower bounds on the minimal batch regret, which is a recently introduced generalization of the average regret, when batches of training data are available to the predictor. As an example, we apply this result to the class of binary memoryless sources. Finally, we generalize the theorem to Rényi information measures, revealing a deep connection between the conditional Rényi divergence and the conditional Sibson's mutual information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10282 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Conditional Regret-Capacity Theorem for Batch Universal Prediction Bondaschi, Marco Gastpar, Michael Information Theory Machine Learning We derive a conditional version of the classical regret-capacity theorem. This result can be used in universal prediction to find lower bounds on the minimal batch regret, which is a recently introduced generalization of the average regret, when batches of training data are available to the predictor. As an example, we apply this result to the class of binary memoryless sources. Finally, we generalize the theorem to Rényi information measures, revealing a deep connection between the conditional Rényi divergence and the conditional Sibson's mutual information. |
| title | The Conditional Regret-Capacity Theorem for Batch Universal Prediction |
| topic | Information Theory Machine Learning |
| url | https://arxiv.org/abs/2508.10282 |