  We propose a novel Bayesian-Optimistic Frequentist Upper Confidence Bound
(BOF-UCB) algorithm for stochastic contextual linear bandits in non-stationary
environments. This unique combination of Bayesian and frequentist principles
enhances adaptability and performance in dynamic settings. The BOF-UCB
algorithm utilizes sequential Bayesian updates to infer the posterior
distribution of the unknown regression parameter, and subsequently employs a
frequentist approach to compute the Upper Confidence Bound (UCB) by maximizing
the expected reward over the posterior distribution. We provide theoretical
guarantees of BOF-UCB's performance and demonstrate its effectiveness in
balancing exploration and exploitation on synthetic datasets and classical
control tasks in a reinforcement learning setting. Our results show that
BOF-UCB outperforms existing methods, making it a promising solution for
sequential decision-making in non-stationary environments.
