RTRA: Rapid Training of Regularization-based Approaches in Continual Learning

Catastrophic forgetting(CF) is a significant challenge in continual learning (CL). In regularization-based approaches to mitigate CF, modifications to important training parameters are penalized in subsequent tasks using an appropriate loss function. We propose the RTRA, a modification to the widely used Elastic Weight Consolidation (EWC) regularization scheme, using the Natural Gradient for loss function optimization. Our approach improves the training of regularization-based methods without sacrificing test-data performance. We compare the proposed RTRA approach against EWC using the iFood251 dataset. We show that RTRA has a clear edge over the state-of-the-art approaches

Analysis of stochastic gradient descent in continuous time

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time representation of stochastic gradient descent. The stochastic gradient process is a dynamical system that is coupled with a continuous-time Markov process living on a finite state space. The dynamical system -- a gradient flow -- represents the gradient descent part, the process on the finite state space represents the random subsampling. Processes of this type are, for instance, used to model clonal populations in fluctuating environments. After introducing it, we study theoretical properties of the stochastic gradient process: We show that it converges weakly to the gradient flow with respect to the full target function, as the learning rate approaches zero. We give conditions under which the stochastic gradient process with constant learning rate is exponentially ergodic in the Wasserstein sense. Then we study the case, where the learning rate goes to zero sufficiently slowly and the single target functions are strongly convex. In this case, the process converges weakly to the point mass concentrated in the global minimum of the full target function; indicating consistency of the method. We conclude after a discussion of discretisation strategies for the stochastic gradient process and numerical experiments