Learning Rate Annealing Improves Tuning Robustness in Stochastic Optimization
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| Format: | Preprint |
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2025
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| author | Attia, Amit Koren, Tomer |
| author_facet | Attia, Amit Koren, Tomer |
| contents | The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a polynomial rate, such as the widely-used cosine schedule, by demonstrating their increased robustness to initial parameter misspecification due to a coarse grid search. We present an analysis in a stochastic convex optimization setup demonstrating that the convergence rate of stochastic gradient descent with annealed schedules depends sublinearly on the multiplicative misspecification factor $ρ$ (i.e., the grid resolution), achieving a rate of $O(ρ^{1/(2p+1)}/\sqrt{T})$ where $p$ is the degree of polynomial decay and $T$ is the number of steps. This is in contrast to the $O(ρ/\sqrt{T})$ rate obtained under the inverse-square-root and fixed stepsize schedules, which depend linearly on $ρ$. Experiments confirm the increased robustness compared to tuning with a fixed stepsize, that has significant implications for the computational overhead of hyperparameter search in practical training scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Rate Annealing Improves Tuning Robustness in Stochastic Optimization Attia, Amit Koren, Tomer Machine Learning Optimization and Control The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a polynomial rate, such as the widely-used cosine schedule, by demonstrating their increased robustness to initial parameter misspecification due to a coarse grid search. We present an analysis in a stochastic convex optimization setup demonstrating that the convergence rate of stochastic gradient descent with annealed schedules depends sublinearly on the multiplicative misspecification factor $ρ$ (i.e., the grid resolution), achieving a rate of $O(ρ^{1/(2p+1)}/\sqrt{T})$ where $p$ is the degree of polynomial decay and $T$ is the number of steps. This is in contrast to the $O(ρ/\sqrt{T})$ rate obtained under the inverse-square-root and fixed stepsize schedules, which depend linearly on $ρ$. Experiments confirm the increased robustness compared to tuning with a fixed stepsize, that has significant implications for the computational overhead of hyperparameter search in practical training scenarios. |
| title | Learning Rate Annealing Improves Tuning Robustness in Stochastic Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2503.09411 |