Reviews: Bayesian Optimization with a Finite Budget: An Approximate Dynamic Programming Approach

I enjoyed this paper where an effort has been made to transfer a relevant formalism and an appropriate technique from the world of Operations Research and Dynamic Programming to Bayesian Optimization. While this was partly done in previous work here it it seems to go one step further, and I am not aware of publications where the Rollout was adapted to this precise problem. The results look promising, especially on the GP realizations, but I really felt the absence of comparison to other strategies recently proposed to adress this very issue; GLASSES of [5] seems a natural competitor here (and maybe also the MCTS of [13]). Also I was wondering if further improvements could be reachable at reasonable research investment regarding the (currently rather simple) base policies. As for the empirical comparisons on functions, the way the models are set appears a bit contrived, and the conclusions would have more weight with some experiments in more realistic conditions.