# Solving Bayesian Risk Optimization via Nested Stochastic Gradient Estimation

arXiv: https://arxiv.org/abs/2007.05860 · HTML: https://mlsanity.com/paper/2007.05860/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency](https://mlsanity.com/paper/2106.12199/) (2021)

## Abstract (arXiv)

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.