在线预测器的最优重新校准

中文摘要 AI 辅助

我们研究了重新校准在线预测器的问题：给定任意的“提示”预测序列，学习者必须输出新的预测，这些预测在重新校准的同时，相对于原始预测的误差增量要小，且在合适损失下。我们给出一个在线算法，能够在T≈ε⁻³轮次内实现（ε，ε²）-重新校准，适用于Lipschitz合适损失。我们证明这种权衡是最佳的，通过证明重新校准对抗平方损失的匹配下界。我们还证明了一个配套的K₂-重新校准定理，其获得的权衡仅相差对数因子。作为主要应用，我们展示了如何将我们的重新校准算法与[FH23]的在线细化方法结合，以在同一渐近速率下实现同时的ε-校准和ε²-校准，优于之前分别实现这些属性或具有更差ε依赖性的作品。特别是，K₂变体回答了[CHJL26]关于同时实现接近最优校准和校准速率的问题。我们还推导了具有多个提示序列的扩展。最后，我们在经历分布转移的分类数据集上经验性地评估了我们的算法。

英文摘要

We study the problem of recalibrating an online predictor [KE17, OKS24]: given an arbitrary "hint" sequence of forecasts, the learner must output new predictions that are calibrated while incurring small excess error relative to the original forecasts, under a proper loss. We give an online algorithm that achieves $(\varepsilon, \varepsilon^2)$-recalibration for Lipschitz proper losses in $T \approx \varepsilon^{-3}$ rounds, using an imbalanced extension of the recent simultaneous Blackwell approachability reduction framework of [HTY26]. We show that this tradeoff is optimal by proving a matching lower bound for recalibrating against the squared loss. We also prove a companion $\mathcal{K}_2$-recalibration theorem that obtains the same tradeoffs up to a logarithmic factor. As our main application, we show how our recalibration algorithms can be combined with the online refinement method of [FH23] to obtain simultaneous $\varepsilon$-calibration and $\varepsilon^2$-calibeating for smooth proper losses at the same asymptotic rate, improving upon prior works that achieved these properties separately or with a worse $\varepsilon$ dependence. In particular, the $\mathcal{K}_2$ variant answers a question of [CHJL26] on simultaneously achieving near-optimal calibeating and calibration rates. We also derive extensions to settings with multiple hint sequences. Finally, we empirically evaluate our algorithms on a classification dataset undergoing distribution shift.

发表机构

• Northeastern University（东北大学）
• University of Texas at Austin（德克萨斯大学奥斯汀分校）

机构由 AI 辅助整理，请以论文原文为准。