Reviews: Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior

The problem of hyperparameters tuning in GPs is indeed relevant. Unfortunately, I do not feel that the work is strong enough, in its current state, to provide clear enough results that other researchers could build upon. I am familiar with the analysis of GP-UCB and with Bayesian optimization. This paper addresses the problem of hyperparameters tuning in Bayesian optimization (e.g. with Gaussian processes). In practice, these hypers are often tuned by maximizing likelihood, at the expense of loosing theoretical guarantees.