ADINE: An Adaptive Momentum Method for Stochastic Gradient Descent

Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum parameter $m$ which is always suggested to be set to less than $1$. Although the choice of $m < 1$ is justified only under very strong theoretical assumptions, it works well in practice even when the assumptions do not necessarily hold. In this paper, we propose a new momentum based method $\textit{ADINE}$, which relaxes the constraint of $m < 1$ and allows the learning algorithm to use adaptive higher momentum. We motivate our hypothesis on $m$ by experimentally verifying that a higher momentum ($\ge 1$) can help escape saddles much faster. Using this motivation, we propose our method $\textit{ADINE}$ that helps weigh the previous updates more (by setting the momentum parameter $> 1$), evaluate our proposed algorithm on deep neural networks and show that $\textit{ADINE}$ helps the learning algorithm to converge much faster without compromising on the generalization error.