Input Warping for Bayesian Optimization of Non-stationary Functions
This addresses the challenge of optimizing hyperparameters in machine learning, where non-stationarity is common, but the approach is incremental as it builds on existing warping techniques.
The paper tackled the problem of optimizing non-stationary functions in Bayesian optimization by developing a method to automatically learn input transformations, resulting in improved performance on benchmark tasks with better results, faster convergence, and greater reliability.
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.