We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a proper loss function corresponding to the negative utility of that individual. For multiple decision makers, our problem can be viewed as a variant of omniprediction in which the goal is to design a single predictor that simultaneously minimizes multiple losses. Existing algorithms for achieving omniprediction broadly fall into two categories: 1) boosting methods that optimize other auxiliary targets such as multicalibration and obtain omniprediction as a corollary, and 2) adversarial two-player game based approaches that estimate and respond to the ``worst-case" loss in an online fashion. We give lower bounds demonstrating that multicalibration is a strictly more difficult problem than omniprediction and thus the former approach must incur suboptimal sample complexity. For the latter approach, we discuss how these ideas can be used to obtain a sample-efficient algorithm through an online-to-batch conversion. This conversion has the downside of returning a complex, randomized predictor. We improve on this method by designing a more direct, unrandomized algorithm that exploits structural elements of the set of proper losses.

翻译：本文研究构建概率预测的问题，该预测在下游用户依据其信息采取行动时能够产生准确的决策。对于单一决策者而言，设计最优预测器等价于最小化与该个体负效用相对应的适当损失函数。对于多决策者情形，我们的问题可视为全预测的一种变体，其目标是设计一个能够同时最小化多种损失的单一预测器。现有的全预测算法主要分为两类：1）通过优化多校准等辅助目标并以此推论获得全预测的增强方法；2）基于对抗性双人博弈的方法，该方法以在线方式估计并响应“最坏情况”损失。我们给出的下界证明多校准是比全预测更困难的问题，因此前一种方法必然产生次优的样本复杂度。对于后一种方法，我们探讨如何通过在线到批处理的转换来获得样本高效的算法。这种转换的缺点在于会返回复杂的随机化预测器。我们通过设计更直接的非随机化算法改进了该方法，该算法利用了适当损失函数集合的结构特性。