Review for NeurIPS paper: Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces

Additional Feedback: Algorithm 2. X_t is never defined. I assumed that X_t is defined by Equation 2 like Algorithm 1. Authors mentioned the same computational budget for acquisition function optimization. What is the optimizer though? Constrained optimization of the acquisition function inside H_t (Equation 3) does not seem trivial. It isn't mentioned anywhere how the acquisition funciton was optimized.