Abstract
We study the discrete dynamics of mini-batch gradient descent with random reshuffling for least squares regression. We show that the training and generalization errors depend on a sample cross-covariance matrix Z between the original features X and a set of new features X̃ in which each feature is modified by the mini-batches that appear before it during the learning process in an averaged way. Using this representation, we establish that the dynamics of mini-batch and full-batch gradient descent agree up to leading order with respect to the step size using the linear scaling rule. However, mini-batch gradient descent with random reshuffling exhibits a subtle dependence on the step size that a gradient flow analysis cannot detect, such as converging to a limit that depends on the step size. By comparing Z, a non-commutative polynomial of random matrices, with the sample covariance matrix of X asymptotically, we demonstrate that batching affects the dynamics by resulting in a form of shrinkage on the spectrum.
Original language | English (US) |
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Pages (from-to) | 736-770 |
Number of pages | 35 |
Journal | Proceedings of Machine Learning Research |
Volume | 272 |
State | Published - 2025 |
Event | 36th International Conference on Algorithmic Learning Theory, ALT 2025 - Milan, Italy Duration: Feb 24 2025 → Feb 27 2025 |
All Science Journal Classification (ASJC) codes
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability