Multi-time Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. In this poster, we establish a novel theoretical connection between the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs, and certain learning problems. Through this novel connection, we increase the interpretability of the training process of certain machine learning applications, by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we establish the connection between the Linear Quadratic Regulator (LQR) and the regularized linear regression problem. We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ODEs) to design new approaches to training methods in learning. Finally, we provide some numerical examples demonstrating the computational advantages of our Riccati-based approach in the context of continual learning, transfer learning, and sparse dynamics identification. This is a joint work with Jerome Darbon (Brown University), George Karniadakis (Brown University), Tingwei Meng (UCLA), and Zongren Zou (Brown University).