Squeeze All: Novel Estimator and Self-Normalized Bound for Linear Contextual Bandits

Autor:	Kim, Wonyoung, Paik, Myunghee Cho, Oh, Min-hwan
Rok vydání:	2022
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We propose a linear contextual bandit algorithm with $O(\sqrt{dT\log T})$ regret bound, where $d$ is the dimension of contexts and $T$ isthe time horizon. Our proposed algorithm is equipped with a novel estimator in which exploration is embedded through explicit randomization. Depending on the randomization, our proposed estimator takes contributions either from contexts of all arms or from selected contexts. We establish a self-normalized bound for our estimator, which allows a novel decomposition of the cumulative regret into \textit{additive} dimension-dependent terms instead of multiplicative terms. We also prove a novel lower bound of $\Omega(\sqrt{dT})$ under our problem setting. Hence, the regret of our proposed algorithm matches the lower bound up to logarithmic factors. The numerical experiments support the theoretical guarantees and show that our proposed method outperforms the existing linear bandit algorithms. Comment: Accepted in Artificial Intelligence and Statistics 2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.05404 Zobrazit plný text záznamu View this record from Arxiv