发表机构
HKUST（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在线二元序贯校准问题，基于已有突破成果，提出结合\textsc{SPR - 校准}程序与外部校正层的随机预测器，实现\(O(T^{2/3 - ε})\)期望校准误差，并对总校准误差进行分解及控制。
AI 中文摘要
我们研究在线二元序贯校准问题。\citet{dagan2024breaking}的一项近期突破克服了校准误差的经典\(T^{2/3}\)障碍。在此结果基础上，我们提出一种高效随机预测器，对于某个常数\(\varepsilon > 0\)，能实现期望校准误差\(O(T^{2/3 - ε})\)。我们的预测器将\textsc{SPR - 校准}程序与外部布莱克威尔式校正层相结合。\textsc{SPR - 校准}程序控制关于条件均值估计的替代序列的校准，校正层控制使用这些替代来近似真实结果时产生的额外误差。分析将总校准误差分解为替代校准误差以及替代序列与真实结果之间的残余差异。前者由\citet{dagan2024breaking}中的\textsc{SPR - 校准}保证界定，后者通过二次势论证以及\textsc{SPR - 校准}预测器的稀疏性来控制。
英文摘要
We study the online binary sequential calibration problem. A recent breakthrough by \citet{dagan2024breaking} overcomes the classical \(T^{2/3}\) barrier for calibration error. Building on this result, we present an efficient randomized forecaster that achieves an expected calibration error \(O(T^{2/3-\varepsilon})\) for some constant \(\varepsilon>0\). Our forecaster combines the \textsc{SPR-Calibration} procedure \citep{dagan2024breaking} with an outer Blackwell-style correction layer. The \textsc{SPR-Calibration} procedure controls calibration with respect to a surrogate sequence of conditional-mean estimates, while the correction layer controls the additional error incurred when these surrogates are used to approximate the true outcomes. The analysis decomposes the total calibration error into the surrogate calibration error and the residual discrepancy between the surrogate sequence and the true outcomes. The former is bounded by the \textsc{SPR-Calibration} guarantee in \citet{dagan2024breaking}, and the latter is controlled using a quadratic potential argument together with the sparsity of the \textsc{SPR-Calibration} forecaster.
