Eluder dimension: localise it!
bernoulli banditsbound recoveryclassic resultscumulative returnseluder dimensionfinite-horizon reinforcement learningfirst-order regret boundsgeneralised linear modelslocalisation methodlower boundmodel classesperformance guaranteesregret analysistask complexity
We establish a lower bound on the eluder dimension in 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.