标题： 输入扭曲用于非平稳函数的贝叶斯优化 显示英文标题

标题： Input Warping for Bayesian Optimization of Non-stationary Functions

摘要： 贝叶斯优化已被证明是一种非常有效的未知、昂贵且多模态函数全局优化方法。准确地对函数分布建模的能力对于贝叶斯优化的有效性至关重要。尽管高斯过程提供了可以高效查询的灵活函数先验，但仍存在各种难以建模的函数类。其中最常见的是非平稳函数类。机器学习算法超参数的优化是一个参数通常需要预先手动转换的问题领域，例如通过在“对数空间”中优化来减轻空间变化长度尺度的影响。我们开发了一种使用Beta累积分布函数自动学习输入空间广泛族的一一变换或扭曲的方法。我们进一步将扭曲框架扩展到多任务贝叶斯优化，以便多个任务可以被扭曲到一个联合平稳的空间。在一组具有挑战性的基准优化任务上，我们观察到加入扭曲大大改进了当前最先进的方法，更快且更可靠地产生更好的结果。 显示英文摘要

摘要： 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.