Papers › Generalized Linear Bandits with Limited Adaptivity

Generalized Linear Bandits with Limited Adaptivity

10 Apr 2024arXiv:2404.06831archive 2025-07-28

Ayush Sawarni, Nirjhar Das, Siddharth Barman, Gaurav Sinha

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 Õ(√(T)) regret when M = Ω( loglogT ) and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm RS-GLinCB that updates its policy Õ(log² T) times and achieves a regret of Õ(√(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.

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