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 measures.

摘要

在本文中，我们旨在解决贝叶斯风险优化（BRO），这是最近提出的框架，用于在输入不确定性下制定仿真优化。为了有效解决BRO问题，我们推导了嵌套的随机梯度估计量，并提出了相应的随机逼近算法。我们证明了梯度估计量是渐近无偏的和一致的，并且算法是渐近收敛的。我们展示了在双面市场模型上算法的经验性能。在将随机梯度估计的文献扩展到嵌套风险度量的情况下，我们的估计器具有独立的兴趣。