Enhancing Optimizer Stability: Momentum Adaptation of The NGN Step-size

2025-08-20

AI Summary

Deep learning optimizers often suffer from poor robustness due to high sensitivity to step-size hyperparameters, leading to costly and labor-intensive tuning. To address this, we propose NGN-M—a novel optimizer that integrates momentum with the NGN step-size adaptation scheme, the first such method requiring neither interpolation conditions nor bounded gradient assumptions. Within a nonconvex stochastic optimization framework, NGN-M achieves an $O(1/sqrt{K})$ convergence rate. Theoretically, it exhibits strong robustness to step-size selection, substantially alleviating hyperparameter dependency. Empirically, NGN-M matches or surpasses state-of-the-art optimizers—including Adam and SGD with momentum—across diverse tasks (e.g., image classification, language modeling) and model architectures. Crucially, it maintains stable convergence over a wide range of step sizes, demonstrating both theoretical rigor and practical effectiveness.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Modern optimization algorithms that incorporate momentum and adaptive step-size offer improved performance in numerous challenging deep learning tasks. However, their effectiveness is often highly sensitive to the choice of hyperparameters, especially the step-size. 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 hyperparameter choices [Schaipp et al., 2024]. In this paper, we introduce an algorithm that matches the performance of state-of-the-art optimizers while improving stability to the choice of the step-size hyperparameter through a novel adaptation of the NGN step-size method [Orvieto and Xiao, 2024]. Specifically, we propose a momentum-based version (NGN-M) that attains the standard convergence rate of $mathcal{O}(1/sqrt{K})$ under less restrictive 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 enhanced robustness to the choice of the step-size hyperparameter while delivering performance that is comparable to or surpasses other state-of-the-art optimizers.

Problem

• Improving optimizer stability to hyperparameter sensitivity
• Reducing step-size tuning difficulty in deep learning
• Enhancing convergence without restrictive gradient assumptions

Innovation

• Momentum-based NGN step-size adaptation
• Enhanced robustness to hyperparameter choices
• Standard convergence rate under relaxed assumptions