Practical Bayesian Optimization for Variable Cost Objectives

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.

[1]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[2]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[3]  Jan Peters,et al.  Bayesian optimization for learning gaits under uncertainty , 2015, Annals of Mathematics and Artificial Intelligence.

[4]  Philipp Hennig,et al.  Entropy Search for Information-Efficient Global Optimization , 2011, J. Mach. Learn. Res..

[5]  Andreas Krause,et al.  Gaussian Process Bandits without Regret: An Experimental Design Approach , 2009, ArXiv.

[6]  Jonas Mockus,et al.  On Bayesian Methods for Seeking the Extremum , 1974, Optimization Techniques.

[7]  Aaron Klein,et al.  Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets , 2016, AISTATS.

[8]  Jasper Snoek,et al.  Multi-Task Bayesian Optimization , 2013, NIPS.

[9]  Matthew W. Hoffman,et al.  Predictive Entropy Search for Efficient Global Optimization of Black-box Functions , 2014, NIPS.

[10]  Tao Wang,et al.  Automatic Gait Optimization with Gaussian Process Regression , 2007, IJCAI.

[11]  Jasper Snoek,et al.  Freeze-Thaw Bayesian Optimization , 2014, ArXiv.

[12]  Howie Choset,et al.  Using response surfaces and expected improvement to optimize snake robot gait parameters , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  Jan Peters,et al.  Bayesian Gait Optimization for Bipedal Locomotion , 2014, LION.

[14]  Thomas J. Santner,et al.  Sequential design of computer experiments to minimize integrated response functions , 2000 .

[15]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[16]  D. Lizotte Practical bayesian optimization , 2008 .

[17]  Ryan P. Adams,et al.  Slice sampling covariance hyperparameters of latent Gaussian models , 2010, NIPS.

[18]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[19]  Tom Minka,et al.  Expectation Propagation for approximate Bayesian inference , 2001, UAI.

[20]  Roman Garnett,et al.  Bayesian optimization for sensor set selection , 2010, IPSN '10.

[21]  Radford M. Neal Slice Sampling , 2003, The Annals of Statistics.