Generalized Linear Bandits with Limited Adaptivity - Sawarni, Ayush; Das, Nirjhar; Barman, Siddharth; Sinha, Gaurav (NeurIPS 2024, 2024)
We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, [B-GLinCB] and [RS-GLinCB], that address, respectively, two prevalent limited adaptivity settings. Given a budget M on the number of policy updates, in the first setting, the algorithm needs to decide upfront M rounds at which it will update its policy, while in the second setting it can adaptively perform M policy updates during its course. For the first setting, we design an algorithm [B-GLinCB], that incurs [O]([T]) regret when M = Ω( [T] ) and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm [RS-GLinCB] that updates its policy [O](^2 T) times and achieves a regret of [O]([T]) even when the arm feature vectors are adversarially generated. Notably, in these bounds, we manage to eliminate the dependence on a key instance dependent parameter κ, that captures non-linearity of the underlying reward model. Our novel approach for removing this dependence for generalized linear contextual bandits might be of independent interest.