On the performance of learned data structures

A recent trend in algorithm design consists of augmenting classic data structures with machine learning models, which are better suited to reveal and exploit patterns and trends in the input data so to achieve outstanding practical improvements in space occupancy and time efficiency. This is especially known in the context of indexing data structures for big data where, despite few attempts in evaluating their asymptotic efficiency, theoretical results are yet missing in showing that learned indexes are provably better than classic indexes, such as B-tree s and their variants. In this paper, we present the first mathematically-grounded answer to this problem by exploiting a link with a mean exit time problem over a proper stochastic process which, we show, is related to the space and time complexity of these learned indexes. As a corollary of this general analysis, we show that plugging this result in the (learned) PGM-index, we get a learned data structure which is provably better than B-tree s.