Both Asymptotic and Non-Asymptotic Convergence of Quasi-Hyperbolic Momentum using Increasing Batch Size

• URL: http://arxiv.org/abs/2506.23544v2
• Date: Tue, 01 Jul 2025 05:38:12 GMT
• Title: Both Asymptotic and Non-Asymptotic Convergence of Quasi-Hyperbolic Momentum using Increasing Batch Size
• Authors: Kento Imaizumi, Hideaki Iiduka,
• Abstract summary: Momentum methods were originally introduced for their superiority to gradientbatch descent (SGD) in deterministic settings with convex functions.<n>We show that achieving convergence requires either a decaying learning rate or an increasing batch size.
• Score: 0.6906005491572401
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Momentum methods were originally introduced for their superiority to stochastic gradient descent (SGD) in deterministic settings with convex objective functions. However, despite their widespread application to deep neural networks -- a representative case of stochastic nonconvex optimization -- the theoretical justification for their effectiveness in such settings remains limited. Quasi-hyperbolic momentum (QHM) is an algorithm that generalizes various momentum methods and has been studied to better understand the class of momentum-based algorithms as a whole. In this paper, we provide both asymptotic and non-asymptotic convergence results for mini-batch QHM with an increasing batch size. We show that achieving asymptotic convergence requires either a decaying learning rate or an increasing batch size. Since a decaying learning rate adversely affects non-asymptotic convergence, we demonstrate that using mini-batch QHM with an increasing batch size -- without decaying the learning rate -- can be a more effective strategy. Our experiments show that even a finite increase in batch size can provide benefits for training neural networks.

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