超越期望：使随机支配成为可能的学习
Beyond Expectations: Learning with Stochastic Dominance Made Practical
AI总结：
本文提出了一种基于随机支配的通用学习框架，通过推广随机支配概念并开发高效计算方法，实现了在多种学习任务中更优的风险权衡。
摘要：
随机支配为在不确定性下建模广泛决策偏好提供了一个通用框架，风险厌恶是其中的一个显著例子，因为它自然捕捉了底层不确定性的内在结构，而不仅仅是依赖期望。尽管在理论上具有吸引力，但随机支配在机器学习中的应用却很少，原因在于以下挑战：i) 原始的随机支配概念仅提供一种偏序，因此不能作为通用的最优性标准；ii) 由于随机支配评估的连续性，缺乏高效的计算方法。在本工作中，我们首次尝试建立一个通用的随机支配学习框架。我们首先将随机支配的概念推广，以使任意任意对随机变量之间能够进行可行的比较。我们接下来开发了一种简单且计算高效的寻找随机支配最优解的方法，该方法可以无缝地应用于许多学习任务。数值实验表明，所提出的方法在性能上与标准风险中性策略相当，并在各种应用中，如监督学习、强化学习和投资组合优化，实现了更好的风险权衡。
英文摘要：
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying uncertainty, in contrast to simply resorting to the expectations. Despite theoretical appeal, the application of stochastic dominance in machine learning has been scarce, due to the following challenges: $\textbf{i)}$, the original concept of stochastic dominance only provides a $\textit{partial order}$, and therefore, is not amenable to serve as a general optimality criterion; and $\textbf{ii)}$, an efficient computational recipe remains lacking due to the continuum nature of evaluating stochastic dominance. In this work, we make the first attempt towards establishing a general framework of learning with stochastic dominance. We first generalize the stochastic dominance concept to enable feasible comparisons between any arbitrary pair of random variables. We next develop a simple and computationally efficient approach for finding the optimal solution in terms of stochastic dominance, which can be seamlessly plugged into many learning tasks. Numerical experiments demonstrate that the proposed method achieves comparable performance as standard risk-neutral strategies and obtains better trade-offs against risk across a variety of applications including supervised learning, reinforcement learning, and portfolio optimization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
