Weighted Sampling for Combined Model Selection and Hyperparameter Tuning

Abstract The combined algorithm selection and hyperparameter tuning (CASH) problem is characterized by large hierarchical hyperparameter spaces. Model-free hyperparameter tuning methods can explore such large spaces efficiently since they are highly parallelizable across multiple machines. When no prior knowledge or meta-data exists to boost their performance, these methods commonly sample random configurations following a uniform distribution. In this work, we propose a novel sampling distribution as an alternative to uniform sampling and prove theoretically that it has a better chance of finding the best configuration in a worst-case setting. In order to compare competing methods rigorously in an experimental setting, one must perform statistical hypothesis testing. We show that there is little-to-no agreement in the automated machine learning literature regarding which methods should be used. We contrast this disparity with the methods recommended by the broader statistics literature, and identify a suitable approach. We then select three popular model-free solutions to CASH and evaluate their performance, with uniform sampling as well as the proposed sampling scheme, across 67 datasets from the OpenML platform. We investigate the trade-off between exploration and exploitation across the three algorithms, and verify empirically that the proposed sampling distribution improves performance in all cases.