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This research establishes a critical lower bound on the eluder dimension for generalized linear models, proving that standard analysis fails to yield first-order regret bounds. By introducing a novel localisation method, the authors successfully recover and improve classic results in Bernoulli bandits while enabling genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.

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Eluder dimension: localise it!

arXiv27 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2601.09825v3 Announce Type: replace 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.

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.

Machine Learning (cs.LG)

arXiv:2601.09825 [cs.LG]

(or arXiv:2601.09825v3 [cs.LG] for this version)

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