Solving Bayesian Risk Optimization via Nested Stochastic Gradient Estimation

TL;DR

This paper introduces nested stochastic gradient estimators and algorithms to efficiently solve Bayesian Risk Optimization problems, demonstrating their convergence and empirical effectiveness in simulation under input uncertainty.

Contribution

The paper develops asymptotically unbiased nested stochastic gradient estimators and algorithms for Bayesian Risk Optimization, extending stochastic gradient methods to nested risk functions.

Findings

Estimators are asymptotically unbiased and consistent.

Algorithms converge asymptotically.

Empirical tests show effective performance on a market model.

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.