Adaptive Momentum Coefficient for Neural Network Optimization.

We propose a novel and efficient momentum-based first-order algorithm for optimizing neural networks which uses an adaptive coefficient for the momentum term. Our algorithm, called Adaptive Momentum Coefficient (AMoC), utilizes the inner product of the gradient and the previous update to the parameters, to effectively control the amount of weight put on the momentum term based on the change of direction in the optimization path. The algorithm is easy to implement and its computational overhead over momentum methods is negligible. Extensive empirical results on both convex and neural network objectives show that AMoC performs well in practise and compares favourably with other first and second-order optimization algorithms. We also provide a convergence analysis and a convergence rate for AMoC, showing theoretical guarantees similar to those provided by other efficient first-order methods.