Solving Bayesian risk optimization via nested stochastic gradient estimation
本文针对输入不确定性下的仿真优化问题，提出嵌套随机梯度估计器及其随机逼近算法，证明其渐近无偏性和一致性，并在双边市场模型中验证了性能。
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.