Bayesian Optimization by Minimum Filling Distance Search

Guang Zhao, Mingqian Li, Raymundo Arroyave, Xiaoning Qian

Keywords: Minimum Filling Distance Search (MFDS), Multi-objective optimization, Pareto front

Abstract: Bayesian Optimization sequentially queries objective function evaluations, often focusing on the expected utility of evaluating corresponding candidates under uncertainty with a learned probabilistic model of underlying true objective functions. We propose a new filling distance based acquisition function, termed Minimum Filling Distance Search (MFDS), to explicitly takes into account the location of the previous queried observations so that acquisition iterations can avoid oversampling and therefore explore the whole design space more efficiently. For multi-objective optimization, in addition to efficiently approaching the Pareto front, the queried candidates by MFDS are well spread over the entire Pareto set. We provide an asymptotical convergence proof and empirically evaluate MFDS performances, demonstrating the improvement over existing methods using other acquisition functions.

Primary Area: optimization

Submission Number: 22962