Solving Bayesian risk optimization via nested stochastic gradient estimation

Abstract

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.

Keywords:

• Simulation optimization
• input uncertainty
• stochastic gradient estimation
• stochastic approximation
• value at risk
• conditional value at risk

Acknowledgments

We thank the anonymous reviewers and the associate editor, whose comments helped improve the presentation of our this article.

Additional information

Funding

The authors gratefully acknowledge the support by the National Science Foundation under Grant CAREER CMMI-1453934, and the Air Force Office of Scientific Research under Grant FA9550-19-1-0283.

Notes on contributors

Sait Cakmak

Sait Cakmak received his BS degrees in industrial engineering and Economics from Koç University, Turkey. He is currently a PhD student in operations research at H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. His research focuses on black-box optimization and simulation optimization.

Di Wu

Di Wu received his BE degree in electrical engineering from East China University of Science and Technology, China, in 2011, a MS degree in control science and engineering from Tsinghua University, China, in 2014, and a PhD degree in operations research from Georgia Institute of Technology in 2019. He currently works as an Applied Scientist at Amazon Web Services.

Enlu Zhou

Enlu Zhou received the BS degree with highest honors in electrical engineering from Zhejiang University, China, in 2004, and a PhD degree in electrical engineering from the University of Maryland, College Park, in 2009. She is currently an associate professor in the School of Industrial & Systems Engineering at Georgia Institute of Technology. Her research interests lie in the theory, methods, and applications of simulation optimization and stochastic control.