Year: 2024
Type: preprint
Abstract: Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying uncertainty, in contrast to simply resorting to the expectations. Despite theoretical appeal, 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 $\textit{partial order}$, and therefore, is not amenable to serve as a general optimality criterion; and $\textbf{ii)}$, an efficient computational recipe remains lacking due to the continuum nature of evaluating stochastic dominance. 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.
Source: arXiv (Cornell University)
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: G1469985387, RINGS: Learning-Enabled Ground and Air Integrated Networks (GAINs), Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning, G8876996369, Collaborative Research: Towards a Theoretic Foundation for Optimal Deep Graph Learning
OpenAlex ID: W4391591287