Introduces a dimension-free Bernstein-type concentration inequality for self-normalised martingales and applies it to ellipsoidal confidence sequences in logistic regression with Hilbert-valued covariates and instance-adaptive regret bounds for Hilbert-armed logistic bandits.
Combining this with our lower bound onlog Mn and upper bound on the log-ratio of normalising constants from Proposition A.4, we obtain the desired result
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Bernstein-type dimension-free concentration for self-normalised martingales
Introduces a dimension-free Bernstein-type concentration inequality for self-normalised martingales and applies it to ellipsoidal confidence sequences in logistic regression with Hilbert-valued covariates and instance-adaptive regret bounds for Hilbert-armed logistic bandits.