多分布学习中预测器存在校准不均问题，需警惕分布间差异。
On Calibration in Multi-Distribution Learning
- 基于损失分解推导出多分布学习最优规则
- 最优解虽最小化最坏情况损失，但校准误差不均
- 揭示校准与精度的内在权衡，适合关注公平性研究者
现代机器学习在鲁棒性、公平性和决策中的挑战催生了多分布学习（MDL）框架，即在多个分布上优化预测器。本文研究MDL的校准性质，以理解预测器在多分布上的统一表现。通过经典可分解合适评分损失的理论，我们推导出MDL的贝叶斯最优规则，证明其最大化相关损失函数的广义熵。分析表明，尽管该方法能最小化最坏情况损失，但仍会导致各分布间校准误差不均，并在贝叶斯最优下存在固有的校准-精炼权衡。结果凸显关键局限：即便在MDL框架下，设计多分布预测器时也必须谨慎，以防分布间差异扩大。
原文摘要 · Abstract (English)
Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the calibration properties of MDL to better understand how the predictor performs uniformly across the multiple distributions. Through classical results on decomposing proper scoring losses, we first derive the Bayes optimal rule for MDL, demonstrating that it maximizes the generalized entropy of the associated loss function. Our analysis reveals that while this approach ensures minimal worst-case loss, it can lead to non-uniform calibration errors across the multiple distributions and there is an inherent calibration-refinement trade-off, even at Bayes optimality. Our results highlight a critical limitation: despite the promise of MDL, one must use caution when designing predictors tailored to multiple distributions so as to minimize disparity.
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