Bayesian optimization with derivatives acceleration

Guillaume Perrin, rodolphe le riche

Abstract:

Bayesian optimization algorithms form an important class of methods to minimize functions that are costly to evaluate, which is a very common situation.
These algorithms iteratively infer Gaussian processes from past observations of the function and decide where new observations should be made
through the maximization of an acquisition criterion.
Often,
the objective function is defined on a compact set such as in a hyper-rectangle of the $d$-dimensional real space,
and the bounds are chosen wide enough so that the optimum is inside the search domain.
In this situation, this work provides a way to integrate in the acquisition criterion the \textit{a priori} information that
these functions, once modeled as GP trajectories, should be evaluated at their minima, and not at any point as usual acquisition criteria do.
We propose an adaptation of the widely used Expected Improvement acquisition criterion that
accounts only for GP trajectories where the first order partial derivatives are zero and the Hessian matrix is positive definite.
The new acquisition criterion keeps an analytical, computationally efficient, expression.
This new acquisition criterion is found to improve Bayesian optimization on a test bed of functions made of Gaussian process trajectories in low dimension problems.
The addition of first and second order derivative information is particularly useful for multimodal functions.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=SlZWTsnx8z

Changes Since Last Submission:

In line with the comments of the TMLR Editors-in-Chief, we are submitting our manuscript in camera-ready mode, having removed the highlights as requested, and having slightly modified the manuscript to incorporate the latest feedback from one of the reviewers.

And we take this opportunity once again to thank all those who gave us feedback on this work, helping us to refine its form and content.

Yours sincerely.

Assigned Action Editor: ~Jasper_Snoek1

Submission Number: 2540