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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.01860 |
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| _version_ | 1866917731507372032 |
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| author | Gorbunov, Eduard Sadiev, Abdurakhmon Danilova, Marina Horváth, Samuel Gidel, Gauthier Dvurechensky, Pavel Gasnikov, Alexander Richtárik, Peter |
| author_facet | Gorbunov, Eduard Sadiev, Abdurakhmon Danilova, Marina Horváth, Samuel Gidel, Gauthier Dvurechensky, Pavel Gasnikov, Alexander Richtárik, Peter |
| contents | High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01860 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise Gorbunov, Eduard Sadiev, Abdurakhmon Danilova, Marina Horváth, Samuel Gidel, Gauthier Dvurechensky, Pavel Gasnikov, Alexander Richtárik, Peter Optimization and Control Machine Learning High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods. |
| title | High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2310.01860 |