Enhancing Optimizer Stability: Momentum Adaptation of The NGNStep-size

Modern optimization algorithms that incorporate momentum and adaptive stepsize offer improved performance in numerous challenging deep learning tasks. However, their effectiveness is often highly sensitive to the choice of hyperparameters, especially the learning rate (LR). Tuning these parameters is often difficult, resource-intensive, and time-consuming. Therefore, recent efforts have been directed toward enhancing the stability of optimizers across a wide range of hyper-parameter choices [79]. In this paper, we introduce an algorithm that matches the performance of state-of-the-art optimizers while improving stability through a novel adaptation of the NGN step-size method [66]. Specifically, we propose a momentum-based version (NGN-M) that attains the standard convergence rate of O(1/ K)under common assumptions, without the need for interpolation condition or assumptions of bounded stochastic gradients or iterates, in contrast to previous approaches. Additionally, we empirically demonstrate that the combination of the NGN step-size with momentum results in high robustness while delivering performance that is comparable to or surpasses other state-of-the-art optimizers.