提出新方法，将在线校准误差降至低于经典上限。
Efficient Sequential Calibration with $O(T^{2/3-ε})$ Error Bound
- 结合代理序列与黑威尔校正层实现高效校准
- 理论误差达 $O(T^{2/3-ε})$，优于旧有 $T^{2/3}$ 上限
- 适合关注在线预测可靠性与理论优化的研究者
我们研究在线二元序列校准问题。近期工作 extcite{dagan2024breaking} 突破了校准误差的经典 $T^{2/3}$ 上限。本文在此基础上，提出一种高效的随机预测器，其期望校准误差为 $O(T^{2/3-ε})$，其中 $ε>0$ 为常数。该预测器结合了 extsc{SPR-Calibration} 过程与外层黑威尔风格校正层：前者控制对代理条件均值序列的校准，后者控制使用代理近似真实结果带来的额外误差。分析将总误差分解为代理校准误差与代理序列和真实结果间的残差差异。前者由 extcite{dagan2024breaking} 的 extsc{SPR-Calibration} 保证，后者通过二次势能论证及 extsc{SPR-Calibration} 预测器的稀疏性加以控制。
原文摘要 · Abstract (English)
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.
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