1. an initial dataset by drawing a size-𝑁 bootstrap sub-sample , i.e., sample with replacement, from the low property value materials 𝑋 (1) , … , 𝑋 (𝑁-⌈𝛼 ̂𝑀⌉-1) and 2. a candidate set consisting of the held-out top ⌈𝛼 ̂𝑀⌉ materials and an up-sampled and stochastically perturbed set 𝑋 ̃1, … , 𝑋 ̃𝑀-⌈𝛼 ̂𝑀⌉ from the unsampled elements of the bootstrap sample. As shown in Figure (bottom left), reward estimation with this approach performs much better than naïve estimation for our bulk modulus example. It accurately predicts GP with EI to produce the highest bulk modulus and highest cumulative reward out of the four candidate methods. As desired, this is based entirely on the initially available data without requiring the over thousand additional calculations that were needed to confirm this result. In-distribution performance is performance with respect to the initial sampling distribution 𝐷 0 , out-of-distribution is with respect to the uniform mixture of the distributions 𝐷 1 to 𝐷 100 of the data points examined by the discovery process. While RF provides a better mean squared error, both in-and out-of-distribution, its out-of-distribution log loss is increasing with the size of the training, indicating a failure of its uncertainty quantification.