In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, the Light Stochastic Dominance Solver (light-SD), that leverages useful properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.

翻译：在实际决策中，不确定性至关重要却难以处理。随机占优为比较不确定性量提供了一种理论上严谨的方法，但带有随机占优约束的优化问题往往计算成本高昂，这限制了其实用性。本文提出了一种简单且高效的求解方法——轻量随机占优求解器（light-SD），该方法利用了拉格朗日函数的有效性质。我们将拉格朗日函数中的内部优化重构为代理近似的学习问题，这绕过了明显的难解性，并实现了可处理的更新甚至梯度计算的闭式解。我们证明了该算法的收敛性并进行了实证检验。所提出的light-SD在从金融到供应链管理的多个代表性问题上展示出优越性能。