A theoretical and empirical study of new adaptive algorithms with additional momentum steps and shifted updates for stochastic non-convex optimization

In the following paper we introduce new adaptive algorithms endowed with momentum terms for stochastic non-convex optimization problems. We investigate the almost sure convergence to stationary points, along with a finite-time horizon analysis with respect to a chosen final iteration, and we also inspect the worst-case iteration complexity. An estimate for the expectation of the squared Euclidean norm of the gradient is given and the theoretical analysis that we perform is assisted by various computational simulations for neural network training.