The page https://www.mathworks.com/help/stats/choose-regression-model-options.html indicates that Regression Learner uses the fitrnet function to train neural networks.
In the algorithms section, the fitrnet page https://www.mathworks.com/help/stats/fitrnet.html indicates "Training Solver: fitrnet uses a limited-memory Broyden-Fletcher-Goldfarb-Shanno quasi-Newton algorithm (LBFGS) [3] as its loss function minimization technique, where the software minimizes the mean squared error (MSE). The LBFGS solver uses a standard line-search method with an approximation to the Hessian."
