Learning to Optimize with Stochastic Dominance Constraints
This addresses a bottleneck in real-world decision-making under uncertainty for domains like finance and supply chain, though it appears incremental as it builds on Lagrangian properties.
The paper tackles the computational expense of optimization with stochastic dominance constraints by developing the Light Stochastic Dominance Solver (light-SD), which recasts inner optimization as a learning problem for surrogate approximation, leading to tractable updates and superior performance on problems in finance and supply chain management.
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.