Eluder dimension: localise it!
Machine Learning
2026-04-21 v2
Abstract
We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.
Cite
@article{arxiv.2601.09825,
title = {Eluder dimension: localise it!},
author = {Alireza Bakhtiari and Alex Ayoub and Samuel Robertson and David Janz and Csaba Szepesvári},
journal= {arXiv preprint arXiv:2601.09825},
year = {2026}
}
Comments
This version corrects a significant error in the published NeurIPS proceedings version. We thank Marc Abeille for bringing the error to our attention