On Global Joint Lower Bounds in Zeroth-Order Nonconvex Optimization
Recent work has sought to transfer first-order nonconvex optimization guarantees to zeroth-order methods through gradient estimators, typically incurring a factor linear in $d$. \citet{kornowski2024} obtained an $\mathcal{O}(dδ^{-1}ε^{-3})$ oracle complexity for nonsmooth nonconvex optimization and asked whether its dependence on all three parameters is jointly optimal. Although the dimension dependence and the first-order dependence on $(δ,ε)$ are separately known to be unavoidable, a matching zeroth-order lower bound has remained open. We answer this question in the unrestricted full-space setting. For smooth stochastic nonconvex optimization, we establish a scalar-oracle lower bound of...
| Authors | Yuxuan Xia, Xiao-Tong Yuan |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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