Learning to Optimize with Stochastic Dominance Constraints
Hanjun Dai, Yuan Xue, Niao He, Yixin Wang, Na Li, Dale Schuurmans, Bo Dai
Abstract
In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach to 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, Light Stochastic Dominance Solver (light-SD), by leveraging properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses the 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.
BibTeX
@InProceedings{pmlr-v206-dai23b,
title = {Learning to Optimize with Stochastic Dominance Constraints},
author = {Dai, Hanjun and Xue, Yuan and He, Niao and Wang, Yixin and Li, Na and Schuurmans, Dale and Dai, Bo},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {8991--9009},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/dai23b/dai23b.pdf},
url = {https://proceedings.mlr.press/v206/dai23b.html},
abstract = {In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach to 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, Light Stochastic Dominance Solver (light-SD), by leveraging properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses the 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.}
}