Dynamic Momentum Recalibration in Online Gradient Learning

2026-03-06

AI Summary

This work addresses the bias-variance imbalance induced by fixed momentum coefficients in gradient-based updates, which often leads to skewed or suboptimal parameter trajectories. Reinterpreting momentum optimization through the lens of signal processing, the paper introduces SGDF, an optimizer that incorporates optimal linear filtering into the momentum mechanism for the first time. By employing online time-varying gains to dynamically recalibrate the momentum coefficient, SGDF minimizes mean squared error and achieves an optimal trade-off between noise suppression and signal fidelity. The method exhibits strong generalizability, seamlessly integrating into existing optimization frameworks, and consistently outperforms conventional momentum-based approaches across diverse model architectures and benchmark tasks, matching or exceeding the performance of state-of-the-art optimizers.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient updates through the lens of signal processing and reveal that fixed momentum coefficients inherently distort the balance between bias and variance, leading to skewed or suboptimal parameter updates. To address this, we propose SGDF (SGD with Filter), an optimizer inspired by the principles of Optimal Linear Filtering. SGDF computes an online, time-varying gain to dynamically refine gradient estimation by minimizing the mean-squared error, thereby achieving an optimal trade-off between noise suppression and signal preservation. Furthermore, our approach could extend to other optimizers, showcasing its broad applicability to optimization frameworks. Extensive experiments across diverse architectures and benchmarks demonstrate SGDF surpasses conventional momentum methods and achieves performance on par with or surpassing state-of-the-art optimizers.

Problem

• Stochastic Gradient Descent
• momentum
• bias-variance trade-off
• gradient estimation
• optimization

Innovation

• Dynamic Momentum Recalibration
• Optimal Linear Filtering
• Online Gradient Estimation
• Bias-Variance Trade-off
• SGDF