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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.03105 |
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| _version_ | 1866909833596239872 |
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| author | Kondo, Yuichi Iiduka, Hideaki |
| author_facet | Kondo, Yuichi Iiduka, Hideaki |
| contents | We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework to cover three practical scheduling strategies commonly used in deep learning: a constant batch size with a decaying learning rate, an increasing batch size with a decaying learning rate, and an increasing batch size with an increasing learning rate. Our results reveal a clear hierarchy in convergence: a constant batch size does not guarantee convergence of the expected gradient norm, whereas an increasing batch size does, and simultaneously increasing both the batch size and learning rate achieves a provably faster decay. Empirical results validate our theory, showing that dynamically scheduled SGDM significantly outperforms its fixed-hyperparameter counterpart in convergence speed. We also evaluated a warm-up schedule in experiments, which empirically outperformed all other strategies in convergence behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerating SGDM via Learning Rate and Batch Size Schedules: A Lyapunov-Based Analysis Kondo, Yuichi Iiduka, Hideaki Machine Learning We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework to cover three practical scheduling strategies commonly used in deep learning: a constant batch size with a decaying learning rate, an increasing batch size with a decaying learning rate, and an increasing batch size with an increasing learning rate. Our results reveal a clear hierarchy in convergence: a constant batch size does not guarantee convergence of the expected gradient norm, whereas an increasing batch size does, and simultaneously increasing both the batch size and learning rate achieves a provably faster decay. Empirical results validate our theory, showing that dynamically scheduled SGDM significantly outperforms its fixed-hyperparameter counterpart in convergence speed. We also evaluated a warm-up schedule in experiments, which empirically outperformed all other strategies in convergence behavior. |
| title | Accelerating SGDM via Learning Rate and Batch Size Schedules: A Lyapunov-Based Analysis |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.03105 |