Beyond Expectations: Learning with Stochastic Dominance Made Practical

Stochastic dominance models risk-averse preferences for decision making withuncertain outcomes, which naturally captures the intrinsic structure of theunderlying uncertainty, in contrast to simply resorting to the expectations.Despite theoretically appealing, the application of stochastic dominance inmachine learning has been scarce, due to the following challenges:i), the original concept of stochastic dominance only provides apartial order, therefore, is not amenable to serve as an optimalitycriterion; and ii), an efficient computational recipe remainslacking due to the continuum nature of evaluating stochastic dominance.barriers its application for machine learning. In this work, we make the first attempt towards establishing a generalframework of learning with stochastic dominance. We first generalize thestochastic dominance concept to enable feasible comparisons between anyarbitrary pair of random variables. We next develop a simple andcomputationally efficient approach for finding the optimal solution in terms ofstochastic dominance, which can be seamlessly plugged into many learning tasks.Numerical experiments demonstrate that the proposed method achieves comparableperformance as standard risk-neutral strategies and obtains better trade-offsagainst risk across a variety of applications including supervised learning,reinforcement learning, and portfolio optimization.