标题： 非平稳函数贝叶斯优化的输入扭曲 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、昂贵且多峰函数全局优化方法。 准确建模函数上的分布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灵活的函数先验，并且可以高效查询，但仍然存在一些难以建模的函数类。 其中最常见的一类是非平稳函数。 机器学习算法超参数的优化问题领域中，通常会手动在先验阶段对参数进行变换，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双射变换或扭曲的方法。 我们进一步将扭曲框架扩展到多任务贝叶斯优化，使多个任务可以被扭曲到联合平稳空间。 在一组具有挑战性的基准优化任务中，我们观察到加入扭曲极大地改进了最先进的方法，更快、更可靠地产生了更好的结果。 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.