Learning Dynamics of Zeroth-Order Optimization: A Kernel Perspective
Classical optimization theory establishes that zeroth-order (ZO) algorithms suffer from a dimension-dependent slowdown, with convergence rates typically scaling with the model dimension compared to first-order methods. However, in contrast to these theoretical expectations, a growing body of recent work demonstrates the successful application of ZO methods to fine-tuning Large Language Models (LLMs) with billions of parameters. To explain this paradox, we derive the one-step learning dynamics of ZO SGD, where the empirical Neural Tangent Kernel (eNTK) naturally emerges as the key term governing the learning behavior. Inspection of the eNTK produced by ZO SGD reveals that each element corr...
| Authors | Zhe Li, Bicheng Ying, Zidong Liu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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