This paper studies the concept of manufacturing systems that autonomously learn how to build parts to a user-specified performance. To perform such a function, these manufacturing systems need to be adaptable to continually change their process or design parameters based on new data, have inline performance sensing to generate data, and have a cognition element to learn the correct process or design parameters to achieve the specified performance. Here, we study the cognition element, investigating a panel of supervised and reinforcement learning machine learning algorithms on a computational emulation of a manufacturing process, focusing on machine learning algorithms that perform well under a limited manufacturing, thus data generation, budget. The case manufacturing study is for the manufacture of an acoustic metamaterial and performance is defined by a metric of conformity with a desired acoustic transmission spectra. We find that offline supervised learning algorithms, which dominate the machine learning community, require an infeasible number of manufacturing observations to suitably optimize the manufacturing process. Online algorithms, which continually modify the parameter search space to focus in on favorable parameter sets, show the potential to optimize a manufacturing process under a considerably smaller manufacturing budget.