Generalized Linear Bandits with Limited Adaptivity

We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, textttB-GLinCB and textttRS-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 textttB-GLinCB, that incurs tildeO(√T) regret when M = Omega( loglog T ) and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm textttRS-GLinCB that updates its policy tildeO(log2 T) times and achieves a regret of tildeO(√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 kappa, 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.