2026-07-28T08:11:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25628 2026-06-23T12:04:04Z ddc:004 open_access

Lower Bounds for the Algorithmic Complexity of Learned Indexes Croquevielle, Luis Alberto Sokolovskii, Roman Heinis, Thomas Learned Indexes Stochastic Processes Approximation Theory Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully understood. We present a framework for proving lower bounds on query time for learned indexes, expressed in terms of their space overhead and parameterized by the model class used for approximation. Our formulation captures a broad family of one-dimensional learned indexes, including most existing designs, as piecewise model-based predictors. We solve the problem of lower bounding query time in two steps: first, we use probabilistic tools to control the effect of sampling when the database attribute is drawn from a probability distribution. Then, we analyze the approximation-theoretic problem of how to optimally represent a cumulative distribution function with approximators from a given model class. Within this framework, we derive lower bounds under a range of modeling and distributional assumptions, paying particular attention to the case of piecewise linear and piecewise constant model classes, which are common in practical implementations. Our analysis shows how tools from approximation theory, such as quantization and Kolmogorov widths, can be leveraged to formalize the space-time trade-offs inherent to learned index structures. The resulting bounds illuminate core limitations of these methods. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Luis Alberto Croquevielle and Roman Sokolovskii and Thomas Heinis 2026 Is Part Of LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICDT.2026.14 urn:nbn:de:0030-drops-256285 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.14 eng https://creativecommons.org/licenses/by/4.0/legalcode