Geometric Moment Contraction for Stochastic Nesterov Acceleration
We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \[ Y_k=Θ_k+β(Θ_k-Θ_{k-1}),\qquad Θ_{k+1}=Y_k-γG(Y_k,X_{k+1}). \] Under mean strong monotonicity and stochastic $L^p$ Lipschitz continuity, an explicit Perron comparison proves synchronous $L^p$ contraction when $βγL_p<(1-β)(1-q_{γ,p})$. This direct criterion includes infinite-variance gradients for $1<p<2$, but its small-step regime requires $β<μ/(μ+L_p)$. A complementary power-Lyapunov argument establishes a positive, generally much smaller, step-size interval for every fixed $β<1$ and every $p>1$, using only a finite $p$th gradient moment. At $p=2$, a simpler explicit certificate gives \[...
| Authors | Wei Biao Wu |
|---|---|
| Primary category | stat.ML |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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