Beyond Expectations: Learning with Stochastic Dominance Made Practical

Abstract: Stochastic dominance models risk-averse preferences for decision making with uncertain outcomes, which naturally captures the intrinsic structure of the underlying uncertainty, in contrast to simply resorting to the expectations. Despite theoretically appealing, the application of stochastic dominance in machine learning has been scarce, due to the following challenges: $\textbf{i)}$, the original concept of stochastic dominance only provides a $\textit{partial order}$, therefore, is not amenable to serve as an optimality criterion; and $\textbf{ii)}$, an efficient computational recipe remains lacking due to the continuum nature of evaluating stochastic dominance.%, which barriers its application for machine learning. In this work, we make the first attempt towards establishing a general framework of learning with stochastic dominance. We first generalize the stochastic dominance concept to enable feasible comparisons between any arbitrary pair of random variables. We next develop a simple and computationally efficient approach for finding the optimal solution in terms of stochastic dominance, which can be seamlessly plugged into many learning tasks. Numerical experiments demonstrate that the proposed method achieves comparable performance as standard risk-neutral strategies and obtains better trade-offs against risk across a variety of applications including supervised learning, reinforcement learning, and portfolio optimization.