Bayesian Optimization (BO) is a method for optimizing expensive-to-evaluate black-box functions.Traditional BO assumes full control over query variables, but in real-world scenarios, controlling certain variables may incur costs.This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS).A new algorithm is proposed for BOCVS with random and unknown costs, achieving sub-linear rate in quality and cost regret.