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:在现实世界的决策中,不确定性很重要,但很难处理。 斯托克控制为比较不确定数量提供了一种理论上合理的方法,但与随机支配地位限制进行优化往往在计算上昂贵,限制了实际适用性。 在本文中,我们为问题制定了简单而有效的方法,即轻小沙控控解决方案(Light-SD),利用拉格朗江人的有用特性。我们把拉格朗江的内部优化重新定位为代孕近似学问题,它绕过明显的易感性,导致可移植的更新,甚至梯度计算封闭式解决方案。我们证明算法的趋同并用经验测试它。 拟议的光控控管显示从金融到供应链管理等若干代表性问题上的优异性表现。</s>