Predicting Block-Coordinate Performance via Cross-Curvature
Simultaneous and sequential block updates are two basic optimization strategies used across machine learning, such as neural-network training, federated learning, and low-rank adaptation. Choosing between them is difficult because their relative advantage depends on both the objective geometry and the number of iterations. We develop a unified theory for comparing Jacobi (JC), Gauss--Seidel (GS), and partially sequential deterministic block-gradient updates. Our analysis expresses the one-step loss difference through cross-block curvature, with an $O(η^3)$ remainder, where $η$ is the learning rate. We derive a signed loss comparison after $K$ iterations with $O(Kη^3)$ error under regulari...
| Authors | Shengkun Zhu, Jinshan Zeng, Zhiqiang Kou et al. |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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