Beyond Expectations: Learning with Stochastic Dominance Made Practical
Shicong Cen Jincheng Mei Hanjun Dai Dale Schuurmans Yuejie Chi Bo Dai
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.