Researchers building behavioral models, such as behavioral game theorists, use experimental data to evaluate predictive models of human behavior. However, there is little agreement about which loss function should be used in evaluations, with error rate, negative log-likelihood, cross-entropy, Brier score, and squared L2 error all being common choices. We attempt to offer a principled answer to the question of which loss functions should be used for this task, formalizing axioms that we argue loss functions should satisfy. We construct a family of loss functions, which we dub "diagonal bounded Bregman divergences", that satisfy all of these axioms. These rule out many loss functions used in practice, but notably include squared L2 error; we thus recommend its use for evaluating behavioral models.

翻译：构建行为模型（例如行为博弈论研究者）的研究人员利用实验数据来评估人类行为的预测模型。然而，对于评估中应使用何种损失函数，目前缺乏共识——错误率、负对数似然、交叉熵、布赖尔分数以及平方L2误差均为常见选择。我们试图为这一问题提供原则性解答，即应选用哪些损失函数来完成该任务，并形式化地提出了我们认为损失函数应满足的公理。我们构造了一类损失函数，称之为“对角有界布雷格曼散度”，这类函数满足所有上述公理。这一结果排除了实践中使用的许多损失函数，但值得注意的是，平方L2误差被包含在内；因此，我们推荐将其用于评估行为模型。