Escaping local minima with derivative-free methods: a numerical investigation

Author: 

Cartis, C
Roberts, L
Sheridan-Methven, O

Last Updated: 

2020-02-02T04:27:08.43+00:00

abstract: 

We apply a state-of-the-art, local derivative-free solver, Py-BOBYQA, to global optimization problems, and propose an algorithmic improvement that is beneficial in this context. Our numerical findings are illustrated on a commonly-used test set of global optimization problems and associated noisy variants, and on hyperparameter tuning for the machine learning test set MNIST. As Py-BOBYQA is a model-based trust-region method, we compare mostly (but not exclusively) with other global optimization methods for which (global) models are important, such as Bayesian optimization and response surface methods; we also consider state-of-the-art representative deterministic and stochastic codes, such as DIRECT and CMA-ES. We find Py-BOBYQA to be competitive with global solvers that are provably designed for finding global optima, for all accuracy/budget regimes, in both smooth and noisy settings. In particular, Py-BOBYQA variants are best performing for smooth and multiplicative noise problems in high-accuracy regimes. As a by-product, some preliminary conclusions can be drawn on the relative performance of the global solvers we have tested with default settings.

Symplectic id: 

1002902

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article