Hypervolume-based Multi-objective Bayesian Optimization with Student-t Processes

Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the hypervolume-based probability of improvement is developed for independent Student-$t$ process priors of the objectives. Its effectiveness is shown on a multi-objective optimization problem which is known to be difficult with traditional Gaussian processes.

[1]  A. O'Hagan,et al.  Bayes–Hermite quadrature , 1991 .

[2]  Andrew Gordon Wilson,et al.  Student-t Processes as Alternatives to Gaussian Processes , 2014, AISTATS.

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

[4]  Tom Dhaene,et al.  Fast Calculation of the Knowledge Gradient for Optimization of Deterministic Engineering Simulations , 2016, ArXiv.

[5]  Tom Dhaene,et al.  Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization , 2014, J. Glob. Optim..

[6]  Lucas Bradstreet,et al.  A Fast Way of Calculating Exact Hypervolumes , 2012, IEEE Transactions on Evolutionary Computation.

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

[8]  Daniel W. Apley,et al.  Local Gaussian Process Approximation for Large Computer Experiments , 2013, 1303.0383.

[9]  Surya T. Tokdar,et al.  Computer Emulation with Nonstationary Gaussian Processes , 2016, SIAM/ASA J. Uncertain. Quantification.

[10]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

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

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

[13]  Daniel Hern'andez-Lobato,et al.  Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints , 2016, Neurocomputing.

[14]  James O. Berger,et al.  Uncertainty analysis and other inference tools for complex computer codes , 1998 .