Convergence Analysis of SGD under Expected Smoothness
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909869506822144 |
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| author | Kawamoto, Yuta Iiduka, Hideaki |
| author_facet | Kawamoto, Yuta Iiduka, Hideaki |
| contents | Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition has emerged as a flexible alternative that ties the second moment of stochastic gradients to the objective value and the full gradient. This paper presents a self-contained convergence analysis of SGD under ES. We (i) refine ES with interpretations and sampling-dependent constants; (ii) derive bounds of the expectation of squared full gradient norm; and (iii) prove $O(1/K)$ rates with explicit residual errors for various step-size schedules. All proofs are given in full detail in the appendix. Our treatment unifies and extends recent threads (Khaled and Richtárik, 2020; Umeda and Iiduka, 2025). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of SGD under Expected Smoothness Kawamoto, Yuta Iiduka, Hideaki Machine Learning Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition has emerged as a flexible alternative that ties the second moment of stochastic gradients to the objective value and the full gradient. This paper presents a self-contained convergence analysis of SGD under ES. We (i) refine ES with interpretations and sampling-dependent constants; (ii) derive bounds of the expectation of squared full gradient norm; and (iii) prove $O(1/K)$ rates with explicit residual errors for various step-size schedules. All proofs are given in full detail in the appendix. Our treatment unifies and extends recent threads (Khaled and Richtárik, 2020; Umeda and Iiduka, 2025). |
| title | Convergence Analysis of SGD under Expected Smoothness |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.20608 |