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Poster
Bayesian Optimization of Composite Functions
Raul Astudillo · Peter I Frazier

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #237
We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we propose a novel approach that exploits the composite structure of the objective function to substantially improve sampling efficiency. Our approach models $h$ using a multi-output Gaussian process and chooses where to sample using the expected improvement evaluated on the implied non-Gaussian posterior on $f$, which we call expected improvement for composite functions (EI-CF). Although EI-CF cannot be computed in closed form, we provide a novel stochastic gradient estimator that allows its efficient maximization. We also show that our approach is asymptotically consistent, i.e., that it recovers a globally optimal solution as sampling effort grows to infinity, generalizing previous convergence results for classical expected improvement. Numerical experiments show that our approach dramatically outperforms standard Bayesian optimization benchmarks, reducing simple regret by several orders of magnitude.

#### Author Information

##### Raul Astudillo (Cornell University)

Raul is a Ph.D. student in the School of Operations Research and Information Engineering at Cornell University, working under the supervision of Prof. Peter Frazier. Previously, he received his B.S. from the Center for Research in Mathematics in Mexico. He is interested in Bayesian optimization, preference elicitation, and their application in complex decision-making.

##### Peter I Frazier (Cornell University / Uber)

Peter Frazier is an Associate Professor in the School of Operations Research and Information Engineering at Cornell University. He is also a Staff Data Scientist at Uber, where he managed the data science group for UberPOOL while on sabbatical leave from Cornell. He completed his Ph.D. in Operations Research and Financial Engineering at Princeton University in 2009. Peter's research is in Bayesian optimization, multi-armed bandits and incentive design for social learning, with applications in e-commerce, the sharing economy, and materials design. He is the recipient of an AFOSR Young Investigator Award and an NSF CAREER Award.