This is achieved via (1) fitting a parameterized material engineering domains where online model on such past data relating the material input experimentation to collect data is too expensive with its output properties; and (2) finding an input optimizer and needs to be replaced by an in silico maximization with respect to the learned parameterization. of a surrogate of the black-box function. Although such a surrogate can be learned from Naively, such in silico approach would trivialize the optimal offline data, its prediction might not be reliable design problem into a vanilla application of gradient outside the offline data regime, which happens ascent and supervised learning. However, in practice, the when the surrogate has narrow prediction margin prediction of such vanilla surrogate might not be reliable and is (therefore) sensitive to small perturbations outside the offline data regime (Fannjiang & Listgarten, of its parameterization. This raises the following 2020). Often, its prediction can become highly erratic at questions: (1) how to regulate the sensitivity out-of-distribution data regimes, misguiding the optimization of a surrogate model; and (2) whether conditioning process toward sub-optimal candidates. This happens an offline optimizer with such less sensitive when the surrogate has narrow prediction margin at those surrogate will lead to better optimization performance.