Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression
Mini-batching is central to large-scale optimization, yet its role in statistical scaling laws remains limited. We study one-pass and multi-pass batch SGD for sketched linear regression under power-law spectral and source conditions. Our analysis reveals a two-horizon phenomenon induced by warmup--stable--decay schedules: deterministic learning is governed by the full optimization trajectory, while stochastic error retains only a shorter terminal memory. For dynamic batch schedules, the individual batch sizes enter through influence-weighted summaries that measure how strongly each update affects the final risk. Consequently, batching leaves the approximation and optimization-bias laws un...
| Authors | Ziyan Chen, Zhongzhu Zhou, Ding-Xuan Zhou |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 15 August 2026 |
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