This paper introduces an objective for optimizing proper scoring rules. The objective is to maximize the increase in payoff of a forecaster who exerts a binary level of effort to refine a posterior belief from a prior belief. In this framework we characterize optimal scoring rules in simple settings, give efficient algorithms for computing optimal scoring rules in complex settings, and identify simple scoring rules that are approximately optimal. In comparison, standard scoring rules in theory and practice -- for example the quadratic rule, scoring rules for the expectation, and scoring rules for multiple tasks that are averages of single-task scoring rules -- can be very far from optimal.

中文翻译：

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评分规则优化

本文介绍了优化适当评分规则的目标。目标是最大化预测者的收益增加，该预测者通过二元努力从先验信念改进后验信念。在这个框架中，我们表征了简单设置中的最优评分规则，给出了计算复杂设置中最优评分规则的有效算法，并确定了近似最优的简单评分规则。相比之下，理论和实践中的标准评分规则——例如二次规则、期望评分规则以及作为单任务评分规则平均值的多任务评分规则——可能远非最佳。