Input Warping for Bayesian Optimization of Non-stationary Functions

TL;DR

This paper introduces a method to automatically learn input transformations using Beta distributions to improve Bayesian optimization of non-stationary functions, leading to faster and more reliable results.

Contribution

It develops a novel input warping technique with Beta distributions and extends it to multi-task optimization, enhancing modeling of non-stationary functions.

Findings

Warping improves optimization speed and reliability.

Method outperforms state-of-the-art on benchmarks.

Automatically learns transformations without manual tuning.

Abstract

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness of Bayesian optimization. Although Gaussian processes provide a flexible prior over functions which can be queried efficiently, there are various classes of functions that remain difficult to model. One of the most frequently occurring of these is the class of non-stationary functions. The optimization of the hyperparameters of machine learning algorithms is a problem domain in which parameters are often manually transformed a priori, for example by optimizing in "log-space," to mitigate the effects of spatially-varying length scale. We develop a methodology for automatically learning a wide family of bijective transformations or warpings of the input space using the Beta cumulative distribution function. We further extend the warping framework to multi-task Bayesian optimization so that multiple tasks can be warped into a jointly stationary space. On a set of challenging benchmark optimization tasks, we observe that the inclusion of warping greatly improves on the state-of-the-art, producing better results faster and more reliably.