The purpose of this work is to compare learning algorithms to identify which is the fastest and most accurate for training mechanical neural networks (MNNs). MNNs are a unique class of lattice-based artificial intelligence (AI) architected materials that learn their mechanical behaviors with repeated exposure to external loads. They can learn multiple behaviors simultaneously in situ and re-learn desired behaviors after being damaged or cut into new shapes. MNNs learn by tuning the stiffnesses of their constituent beams similar to how artificial neural networks (ANNs) learn by tuning their weights. In this work, we compare the performance of six algorithms (i.e., genetic algorithm, full pattern search, partial pattern search, interior point, sequential quadratic progression, and Nelder–Mead) applied to MNN leaning. A computational model was created to simulate MNN learning using these algorithms with experimentally measured noise included. A total of 3900 runs were simulated. The results were validated using experimentally collected data from a physical MNN. We identify algorithms like Nelder–Mead that are both fast and able to reject noise. Additionally, we provide insights into selecting learning algorithms based on the desired balance between accuracy and speed, as well as the general characteristics that are favorable for training MNNs. These insights will promote more efficient MNN learning and will provide a foundation for future algorithm development.