Tight Stochastic Condition-Number Dependence in Nonconvex-Strongly-Concave Minimax Optimization
We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization. For jointly $L$-smooth objectives with dual strong-concavity parameter $μ$, we prove a lower bound that matches the SAPD+ upper bound under the same Moreau-envelope stationarity criterion and the same primal-dual initialization gap. Specifically, when $σ\ge\varepsilon$, the worst-case complexity of zero-respecting algorithms is $Θ(κLGσ^2\varepsilon^{-4})$ in the stated accuracy regime, where $κ=L/μ$, $G$ bounds the initial primal-dual gap, and $σ^2$ bounds the variance of a general unbiased first-order oracle. The lower bound is re...
| Authors | Qihao Zhou |
|---|---|
| Primary category | math.OC |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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