Solving Bayesian risk optimization via nested stochastic gradient estimation. (3rd October 2021)

• Record Type: Journal Article
• Authors: Cakmak, Sait; Wu, Di; Zhou, Enlu
• Is Part Of: IISE transactions. Volume 53:Number 10(2021)
• Page Start: 1081
• Page End: 1093
• Publication Date: 2021-10-03
• Subjects: Simulation optimization -- input uncertainty -- stochastic gradient estimation -- stochastic approximation -- value at risk -- conditional value at risk; Industrial engineering -- Periodicals; Systems engineering -- Periodicals; Industrial engineering; Systems engineering; Electronic journals; Periodicals; 670.285
• DOI: Https://www.tandfonline.com/doi/10.1080/24725854.2020.1869352
• Languages: English
• ISSNs: 2472-5854

Abstract

Abstract: In this article, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested stochastic gradient estimators and propose corresponding stochastic approximation algorithms. We show that our gradient estimators are asymptotically unbiased and consistent, and that the algorithms converge asymptotically. We demonstrate the empirical performance of the algorithms on a two-sided market model. Our estimators are of independent interest in extending the literature of stochastic gradient estimation to the case of nested risk measures.