  AutoML platforms have numerous options for the algorithms to try for each
step of the analysis, i.e., different possible algorithms for imputation,
transformations, feature selection, and modelling. Finding the optimal
combination of algorithms and hyper-parameter values is computationally
expensive, as the number of combinations to explore leads to an exponential
explosion of the space. In this paper, we present the Sequential
Hyper-parameter Space Reduction (SHSR) algorithm that reduces the space for an
AutoML tool with negligible drop in its predictive performance. SHSR is a
meta-level learning algorithm that analyzes past runs of an AutoML tool on
several datasets and learns which hyper-parameter values to filter out from
consideration on a new dataset to analyze. SHSR is evaluated on 284
classification and 375 regression problems, showing an approximate 30%
reduction in execution time with a performance drop of less than 0.1%.
