All four reviewers were in favor of accepting this paper. Despite the fact that this paper is not very dense in terms of methodological contributions, the reviewers appreciated the simplicity of the idea, which also gives good results. Indeed, amortization for the hyperparameters of the GP has not been considered before, and seems like a neat solution to the key problem of learning GP models. Furthermore, the reviewers appreciate the potential applicability of this method, e.g. to Bayesian Optimization.