Control Theoretic Approach to Fine-Tuning and Transfer Learning

Given a training set in the form of a paired (X,Y), we say that the control system dot x = f(x,u) has learned the paired set via the control u^* if the system steers each point of X to its corresponding target in Y. If the training set is expanded, most existing methods for finding a new control u^* require starting from scratch, resulting in a quadratic increase in complexity with the number of points. To overcome this limitation, we introduce the concept of textit tuning without forgetting. We develop textitan iterative algorithm to tune the control u^* when the training set expands, whereby points already in the paired set are still matched, and new training samples are learned. At each update of our method, the control u^* is projected onto the kernel of the end-point mapping generated by the controlled dynamics at the learned samples. It ensures keeping the end-points for the previously learned samples constant while iteratively learning additional samples.