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Bayesian Optimization of Function Networks
Raul Astudillo · Peter Frazier

Wed Dec 08 04:30 PM -- 06:00 PM (PST) @ None #None

We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in reinforcement learning, engineering design, and manufacturing. While the standard Bayesian optimization approach observes only the final output, our approach delivers greater query efficiency by leveraging information that the former ignores: intermediate output within the network. This is achieved by modeling the nodes of the network using Gaussian processes and choosing the points to evaluate using, as our acquisition function, the expected improvement computed with respect to the implied posterior on the objective. Although the non-Gaussian nature of this posterior prevents computing our acquisition function in closed form, we show that it can be efficiently maximized via sample average approximation. In addition, we prove that our method is asymptotically consistent, meaning that it finds a globally optimal solution as the number of evaluations grows to infinity, thus generalizing previously known convergence results for the expected improvement. Notably, this holds even though our method might not evaluate the domain densely, instead leveraging problem structure to leave regions unexplored. Finally, we show that our approach dramatically outperforms standard Bayesian optimization methods in several synthetic and real-world problems.

Author Information

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.

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