提出批量通用预测的条件化后悔-容量定理，揭示其理论下限。
The Conditional Regret-Capacity Theorem for Batch Universal Prediction
- 基于条件化分析，推导出批量预测的最小后悔下界。
- 在二元无记忆信源上验证，给出具体后悔下界值。
- 推广至Rényi信息测度，揭示新信息论联系。
我们推导了经典后悔-容量定理的条件版本。该结果可用于通用预测中，确定当预测器可获得批量训练数据时，最小批量后悔的下界——这是平均后悔的一种新近推广。作为应用，我们将该结果应用于二元无记忆信源类。最后，我们进一步将定理推广至Rényi信息测度，揭示了条件Rényi散度与条件Sibson互信息之间的深层联系。
原文摘要 · Abstract (English)
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.
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