Momentum SGD incurs a provable drift-amplification penalty in nonstationary stochastic optimization that makes it worse than vanilla SGD in drift-dominated regimes, confirmed by finite-time upper bounds and minimax lower bounds under gradient-variation constraints.
Then ξt+1(θ) is Ft+1–measurable and satisfies E[ξt+1(θ)| Ft] =0a.s
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On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization
Momentum SGD incurs a provable drift-amplification penalty in nonstationary stochastic optimization that makes it worse than vanilla SGD in drift-dominated regimes, confirmed by finite-time upper bounds and minimax lower bounds under gradient-variation constraints.