  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.
