In this work, we consider the notion of "criterion collapse," in which optimization of one metric implies optimality in another, with a particular focus on conditions for collapse into error probability minimizers under a wide variety of learning criteria, ranging from DRO and OCE risks (CVaR, tilted ERM) to non-monotonic criteria underlying recent ascent-descent algorithms explored in the literature (Flooding, SoftAD). We show how collapse in the context of losses with a Bernoulli distribution goes far beyond existing results for CVaR and DRO, then expand our scope to include surrogate losses, showing conditions where monotonic criteria such as tilted ERM cannot avoid collapse, whereas non-monotonic alternatives can.

翻译：本文探讨了“准则坍缩”的概念，即某一指标的优化隐含着另一指标的最优性，特别关注在多种学习准则（从DRO和OCE风险（CVaR、倾斜ERM）到文献中探索的最新上升-下降算法（Flooding、SoftAD）所基于的非单调准则）下，坍缩为误差概率最小化器的条件。我们展示了在伯努利分布损失背景下，坍缩现象远超现有针对CVaR和DRO的研究成果，随后将范围扩展至替代损失，揭示了单调准则（如倾斜ERM）无法避免坍缩的条件，而非单调替代准则则能规避这一问题。