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Bayesian Optimization of Risk Measures
Sait Cakmak · Raul Astudillo · Peter Frazier · Enlu Zhou

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1601
We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness induced by the environmental random variable $W$. Such problems arise in decision making under uncertainty, such as in portfolio optimization and robust systems design. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency. Instead of modeling the objective function directly as is typical in Bayesian optimization, these algorithms model $F$ as a Gaussian process, and use the implied posterior on the objective function to decide which points to evaluate. We demonstrate the effectiveness of our approach in a variety of numerical experiments.

Author Information

Sait Cakmak (Georgia Institute of Technology)
Raul Astudillo (Cornell University)

I am a Ph.D. candidate in the School of Operations Research and Information Engineering at Cornell University, where I am fortunate to be advised by Professor Peter Frazier. Prior to coming to Cornell, I completed the undergraduate program in Mathematics offered jointly by the University of Guanajuato and the Center for Research in Mathematics. My current research focuses on the design and analysis of Bayesian optimization algorithms for problems with nested objective functions.

Peter Frazier (Cornell / Uber)

Peter Frazier is an Associate Professor in the School of Operations Research and Information Engineering at Cornell University, and a Staff Data Scientist at Uber. He received a Ph.D. in Operations Research and Financial Engineering from Princeton University in 2009. His research is at the intersection of machine learning and operations research, focusing on Bayesian optimization, multi-armed bandits, active learning, and Bayesian nonparametric statistics. He is an associate editor for Operations Research, ACM TOMACS, and IISE Transactions, and is the recipient of an AFOSR Young Investigator Award and an NSF CAREER Award.

Enlu Zhou (Georgia Institute of Technology)

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