Reviews: Lookahead Bayesian Optimization with Inequality Constraints

This paper seems a continuation of last year: Bayesian optimization with a finite budget... where the authors have added new elements to deal with inequality constraints. The method uses a approximation of a lookahead strategy by dynamic programming. For the constrained case, the authors propose an heuristic that combines the EIc criterion for all the steps except for the last one were the mean function is used. The authors claim that the mean function has an exploitative behaviour, although it has been previously shown that it might be misleading [A]. A considerably amount of the text, including Figure 1, can be mostly found in [16]. Although it is nice to have an self-contained paper as much as possible, that space could be used to explain better the selection of the acquisition heuristic and present alternatives.