Ordinary Nonconvex SGD under Distance-Dependent Moments: Finite-Horizon Stationarity and Nagaev Bounds
Uniform noise-moment bounds exclude stochastic gradients whose variability increases with the iterate. We study ordinary, single-sample stochastic gradient descent for smooth, lower-bounded, possibly nonconvex objectives under distance-dependent conditional moments. Under second moments alone, a direct descent--displacement argument yields $T^{-1/3}$ expected average squared-gradient stationarity with a horizon-dependent stepsize. An explicit oracle-complexity corollary matches the known smooth Blum--Gladyshev (BG-0) lower bound, including the $Lb_2Δ^3\varepsilon^{-6}$ and $LΔσ^2\varepsilon^{-4}$ stochastic terms, where $Δ$ is the initial objective gap and $σ^2+b_2\|x-x_1\|^2$ bounds the ...
| Authors | Wei Biao Wu |
|---|---|
| Primary category | stat.ML |
| Published | 24 September 2026 |
| Last updated at source | 7 October 2026 |
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