Bayesian Functional Optimization

Ngo Anh Vien, Heiko Zimmermann, Marc Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)
121 Downloads (Pure)


Bayesian optimization (BayesOpt) is a derivative-free ap-proach for sequentially optimizing stochastic black-box functions. Standard BayesOpt, which has shown many successesin machine learning applications, assumes a finite dimen-sional domain which often is a parametric space. The pa-rameter space is defined by the features used in the function approximations which are often selected manually. There-fore, the performance of BayesOpt inevitably depends onthe quality of chosen features. This paper proposes a newBayesian optimization framework that is able to optimize di-rectly on the domain of function spaces. The resulting frame-work, Bayesian Functional Optimization (BFO), not only ex-tends the application domains of BayesOpt to functional op-timization problems but also relaxes the performance depen-dency on the chosen parameter space. We model the domainof functions as a reproducing kernel Hilbert space (RKHS),and use the notion of Gaussian processes on a real separa-ble Hilbert space. As a result, we are able to define tradi-tional improvement-based (PI and EI) and optimistic acquisi-tion functions (UCB) as functionals. We propose to optimizethe acquisition functionals using analytic functional gradientsthat are also proved to be functions in a RKHS. We evaluateBFO in three typical functional optimization tasks: i) a syn-thetic functional optimization problem, ii) optimizing activa-tion functions for a multi-layer perceptron neural network,and iii) a reinforcement learning task whose policies are mod-eled in RKHS.
Original languageEnglish
Title of host publicationThe Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18)
Number of pages8
Publication statusPublished - 29 Apr 2018
EventAAAI 2018 - New Orleans, New Orleans, United States
Duration: 02 Feb 201807 Feb 2018

Publication series

NameProceedings Of The AAAI Conference On Artificial Intelligence And The Innovative Applications Of Artificial Intelligence Conference
ISSN (Print)2159-5399
ISSN (Electronic)2374-3468


ConferenceAAAI 2018
Country/TerritoryUnited States
CityNew Orleans
Internet address


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