text: Many black-box optimization problems are "multi-fidelity", in which it is possible to acquire data with different levels of cost and associated uncertainty. The training of machine learning models is a common example, in which more data and/or more training may lead to more precise measurements of the quality of a hyperparameter configuration. This has previously been referred to as a special case of "multi-task" Bayesian optimization, in which the tasks can be constructed to reflect different fidelities. The present paper examines this construction with three twists: using the knowledge gradient acquisition function, using batched function evaluations, and incorporating derivative observations. Broadly speaking, the idea is to allow fidelity to be represented as a point in a hypercube and then include this hypercube as a covariate in the Gaussian process. The knowledge gradient acquisition function then becomes "knowledge gradient per unit cost" the KG equivalent to the "expected improvement per unit cost" discussed in Snoek et al (2012), although that paper did not consider treating fidelity separately. I don't understand the claim that this is "the first multi-fidelity algorithm that can leverage gradients". Can't any Gaussian process model use gradient observations trivially, as discussed in the Rasmussen and Williams book? Why can't any EI or entropy search method also use gradient observations? This doesn't usually come up in hyperparameter optimization, but it seems like a grandiose claim. Similarly, although I don't know of a paper that explicitly does "A + B" for multi-fidelity BO and parallel BO, it is an incremental contribution to combine them, not least because no other parallel BO methods get evaluated as baselines. Figure 1 does not make sense to me. How can the batched algorithm outperform the sequential algorithm on total cost? The sequential cfKG algorithm should always be able to make better decisions with its remaining budget than 8-cfKG. Is the answer that "cost" here means "wall-clock time when parallelism is available"? If that's the case, then it is necessary to include plots of parallelized EI, entropy search, and KG. The same is true for Figure 2; other parallel BO algorithms need to appear.