The Conditional Regret-Capacity Theorem for Batch Universal Prediction

Marco Bondaschi; Michael Gastpar

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arXiv · 2508.10282

The Conditional Regret-Capacity Theorem for Batch Universal Prediction

Marco Bondaschi·Michael Gastpar

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Abstract

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 R\'enyi information measures, revealing a deep connection between the conditional R\'enyi divergence and the conditional Sibson's mutual information.

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Marco Bondaschi, Michael Gastpar. 2025-08-14. The Conditional Regret-Capacity Theorem for Batch Universal Prediction. https://arxiv.org/abs/2508.10282

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