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arXiv 2511.13699cs.LGcs.DSstat.ML
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面向决策的高效校准

Efficient Calibration for Decision Making

Apple(苹果公司);UT Austin(得克萨斯大学奥斯汀分校);Harvard(哈佛大学)

Parikshit Gopalan, Konstantinos Stavropoulos, Kunal Talwar, Pranay Tankala

AI总结:

针对现有校准决策损失$\mathsf{CDL}$离线近似难算的问题,提出限定结构化后处理族的$\mathsf{CDL}_K$度量,建立其可解性理论并推导边界,为常用重校准流程提供严格保证。

摘要:

完美校准的决策论刻画是:对于期望最小化恰当损失的智能体,对完美校准的预测器进行后处理无法提升其结果。Hu和Wu(FOCS'24)基于此定义了名为校准决策损失($\mathsf{CDL}$)的近似校准度量,该度量衡量任意后处理在任意恰当损失上可实现的最大提升。遗憾的是,在离线场景下,当仅能通过黑盒访问预测结果与标签时,$\mathsf{CDL}$ 即便进行弱近似也难以计算。我们提出通过将关注点限制在结构化后处理函数族 $K$ 上来规避这一难题。我们定义了相对于 $K$ 的校准决策损失,记为 $\mathsf{CDL}_K$,该度量考虑所有恰当损失,但将后处理限制在结构化族 $K$ 内。我们建立了完备的理论,明确 $\mathsf{CDL}_K$ 在信息论与计算层面可解的条件,并基于此证明了自然类 $K$ 对应的上下界。除了为面向决策的校准理论引入新定义与算法技术外,我们的研究结果还为机器学习中部分广泛使用的重校准流程提供了严格的理论保证。

英文摘要:

A decision-theoretic characterization of perfect calibration is that an agent seeking to minimize a proper loss in expectation cannot improve their outcome by post-processing a perfectly calibrated predictor. Hu and Wu (FOCS'24) use this to define an approximate calibration measure called calibration decision loss ($\mathsf{CDL}$), which measures the maximal improvement achievable by any post-processing over any proper loss. Unfortunately, $\mathsf{CDL}$ turns out to be intractable to even weakly approximate in the offline setting, given black-box access to the predictions and labels. We suggest circumventing this by restricting attention to structured families of post-processing functions $K$. We define the calibration decision loss relative to $K$, denoted $\mathsf{CDL}_K$ where we consider all proper losses but restrict post-processings to a structured family $K$. We develop a comprehensive theory of when $\mathsf{CDL}_K$ is information-theoretically and computationally tractable, and use it to prove both upper and lower bounds for natural classes $K$. In addition to introducing new definitions and algorithmic techniques to the theory of calibration for decision making, our results give rigorous guarantees for some widely used recalibration procedures in machine learning.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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