2022/11/14 by Hanjun Dai, Dai, Hanjun, Yuan Xue +11
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2211.07767
openalex publication_date 2022/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.