Eluder dimension: localise it!

Alireza Bakhtiari, Alex Ayoub, Samuel Robertson, David Janz, Csaba Szepesvári
1/14/2026
cs.LG

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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.

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Cite this paper

@article{bakhtiari2026eluder,
  title  = {Eluder dimension: localise it!},
  author = {Alireza Bakhtiari and Alex Ayoub and Samuel Robertson and David Janz and Csaba Szepesvári},
  year   = {2026},
  eprint = {2601.09825},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2601.09825v1}
}

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