Solving Bayesian Risk Optimization via Nested Stochastic Gradient Estimation

Abstract

In this paper, 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 functions.

The paper is 20 pages with 3 figures. The supplement is an additional 15 pages. The paper is currently under review at IISE Transactions. Updated formatting in v2