Convergence Analysis of Randomized Subspace Normalized SGD under Heavy-Tailed Noise
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914288713596928 |
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| author | Omiya, Gaku Poirion, Pierre-Louis Takeda, Akiko |
| author_facet | Omiya, Gaku Poirion, Pierre-Louis Takeda, Akiko |
| contents | Randomized subspace methods reduce per-iteration cost; however, in nonconvex optimization, most analyses are expectation-based, and high-probability bounds remain scarce even under sub-Gaussian noise. We first prove that randomized subspace SGD (RS-SGD) admits a high-probability convergence bound under sub-Gaussian noise, achieving the same order of oracle complexity as prior in-expectation results. Motivated by the prevalence of heavy-tailed gradients in modern machine learning, we then propose randomized subspace normalized SGD (RS-NSGD), which integrates direction normalization into subspace updates. Assuming the noise has bounded $p$-th moments, we establish both in-expectation and high-probability convergence guarantees, and show that RS-NSGD can achieve better oracle complexity than full-dimensional normalized SGD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of Randomized Subspace Normalized SGD under Heavy-Tailed Noise Omiya, Gaku Poirion, Pierre-Louis Takeda, Akiko Optimization and Control Machine Learning 90C30 (Primary), 90C06, 60B20 (Secondary) Randomized subspace methods reduce per-iteration cost; however, in nonconvex optimization, most analyses are expectation-based, and high-probability bounds remain scarce even under sub-Gaussian noise. We first prove that randomized subspace SGD (RS-SGD) admits a high-probability convergence bound under sub-Gaussian noise, achieving the same order of oracle complexity as prior in-expectation results. Motivated by the prevalence of heavy-tailed gradients in modern machine learning, we then propose randomized subspace normalized SGD (RS-NSGD), which integrates direction normalization into subspace updates. Assuming the noise has bounded $p$-th moments, we establish both in-expectation and high-probability convergence guarantees, and show that RS-NSGD can achieve better oracle complexity than full-dimensional normalized SGD. |
| title | Convergence Analysis of Randomized Subspace Normalized SGD under Heavy-Tailed Noise |
| topic | Optimization and Control Machine Learning 90C30 (Primary), 90C06, 60B20 (Secondary) |
| url | https://arxiv.org/abs/2601.20399 |