*PROS: extension of multi-fidelity max value entropy search from Gaussian processes to neural networks *CONS: there are concern is about the choice of hyper-parameters for the neural network, The proposed method seems rather complicated and involved with concerns for reproducibility, small scale evaluation Meta-reviewer recommendations: The paper is clearly borderline with R1 and R2 voting for acceptance and R3 and R4 leaning towards rejection. R3 seems overly negative in a not very well justified manner. R4's review is very short and mainly indicates that the difference to the multi-fidelity modeling proposed by Cutajar et al (2019) should be made clear. I believe the authors successfully address R4's comments in the rebuttal. I recommend the authors to perform an ablation study recommended by R3 in their final version. As recommended, the experiments should be further improved based on the reviews. The method seems heavily dependent on the approximations and hyper-parameters, the implementation details should be provided or the code should be released for reproducibility.