Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles
Stochastic nonconvex optimization is central to training deep networks and LLMs in modern machine learning. We give a black-box reduction from stochastic nonconvex optimization to ordinary static regret minimization in online convex optimization (OCO), thereby resolving the open problem posed by Chen and Hazan (2024). Our reduction maintains a predictable gradient tracker, while a black-box online learner $\mathcal{A}$ selects a preconditioner that transforms this tracker into the update direction. Given a \(β\)-smooth function with a range bounded by $M$ and an unbiased gradient oracle with variance bounded by $σ^2$, we bound the expected average squared gradient norm by $O(σ\sqrt{Mβ/T}+...
| Authors | Haichen Hu, David Simchi-Levi |
|---|---|
| Primary category | cs.LG |
| Published | 20 July 2026 |
| Last updated at source | 16 September 2026 |
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