Study Shows Full-Batch Gradient Descent More Sample-Efficient Than One-Pass SGD in Nonlinear Learning
A new theoretical study demonstrates that full-batch gradient descent outperforms one-pass stochastic gradient descent in sample complexity for learning single-index models with nonlinear activations. The research shows that while one-pass SGD requires roughly d log d samples, full-batch GD with activation truncation achieves recovery with approximately d samples. This finding extends understanding of multi-pass gradient descent benefits beyond linear settings to nonlinear and non-convex optimization problems.
Researchers have established a theoretical separation in sample complexity between full-batch gradient descent (GD) and one-pass stochastic gradient descent (SGD) for learning d-dimensional single-index models with quadratic activations. While it is generally accepted that reusing training data improves statistical efficiency, this benefit has been well-understood primarily in linear regression. The study shows that one-pass SGD requires n ≳ d log d samples for weak recovery, whereas full-batch GD with a truncated activation function achieves favorable optimization landscape properties at n ≃ d samples. Additionally, trajectory analysis demonstrates that full-batch GD on the squared loss requires approximately d samples and log d gradient steps for strong exact recovery from small initialization. These results provide new theoretical insights into the advantages of multi-pass gradient descent in nonlinear and non-convex settings.
What's missing
The study does not discuss computational complexity or wall-clock time comparisons between full-batch GD and one-pass SGD, focusing instead on sample complexity. The practical implications for real-world machine learning applications with finite computational budgets remain unaddressed. Additionally, the generalization of these results beyond single-index models to broader classes of nonlinear functions is not explored.
What different sources said
- arXiv cs.LGCenter
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