Zeroth-Order Optimization at the Edge of Stability
Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored. In this work, we provide an explicit step size condition that exactly captures the (mean-square) linear stability of a family of ZO methods based on the standard two-point estimator. Our characterization reveals a sharp contrast with first-order (FO) methods: whereas FO stability is governed solely by the largest Hessian eigenvalue, mean-square stability of ZO methods depends on the entire Hessian spectrum. Since computing the full Hessian sp...
| Authors | Minhak Song, Liang Zhang, Bingcong Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 April 2026 |
| Last updated at source | 1 July 2026 |
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