证明了序列预测中精确诚实校准不可行，提出两种近似诚实的新方法。
Truthful Calibration Measures for Sequential Prediction
- 通过归约构造加法和乘法近似诚实的校准度量
- 在独立事件下仍无法实现完全诚实校准
- 新方法比前人更优，适合在线预测场景
校准要求概率报告条件无偏且可解释为概率。校准度量为误校准报告分配数值误差。Haghtalab 等（2024）提出了在线预测中的近似诚实校准度量，但未解决精确诚实是否与完备性和合理性相容的问题。本文针对序列二元预测问题，否定性回答该问题：即使在独立结果条件下，精确诚实也与完备性和合理性不相容。随后证明此不可能性仅针对精确诚实。我们给出两种从基础校准度量出发的通用归约，分别生成加法和乘法近似诚实的校准度量。应用乘法归约，对任意 $0 < heta < 1$，构造出一个既合理又完备的校准度量，其乘法诚实性达到 $(1+ ext{exp}(-T^{(1- heta)/2}/2))$，优于 Haghtalab 等（2024）的近似诚实保证。
原文摘要 · Abstract (English)
Calibration requires probabilistic reports to be conditionally unbiased and reliably interpretable as probabilities. A calibration measure assigns numerical error to miscalibrated reports. Haghtalab et al. (2024) proposed an approximately truthful calibration measure for online prediction, leaving open whether exact truthfulness is compatible with completeness and soundness. We resolve this question negatively for sequential binary prediction: exact truthfulness is incompatible with completeness and soundness, even for independent outcomes. We then show that this impossibility is specific to exact truthfulness. We give two general reductions from a base calibration measure, producing additively and multiplicatively approximately truthful calibration measures, respectively. Applying the multiplicative reduction, for every $0 < \varepsilon < 1$ we construct a sound and complete calibration measure that is $(1+\exp(-T^{(1-\varepsilon)/2}/2))$-multiplicatively truthful. This improves the approximate-truthfulness guarantee of Haghtalab et al. (2024).
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