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.
Furthermore, for eachn ∈ N+, let ¯M0 = 1 and ¯Mn := ¯Mn(πn|B) and define Jn(x) = ⟨Sn, x⟩ − ⟨x, Hnx⟩/2
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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.