2024/04/10 by Sawarni, Ayush, Das, Nirjhar, Barman, Siddharth +1 · 6 citations
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · doi:10.48550/arxiv.2404.06831
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( loglog T ) and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm RS-GLinCB that updates its policy O(log2 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.