(37) (i) Now, we provide the upper bound of E∥xt − xt− 1 2 ∥2 F

The proof of Lemma 3 From (27d)–(27e), we have E∥xt − ˆxt∥2 F = E∥xt − (ˆxt− 1 + C(xt− 1 2 − ˆxt− 1))∥2 F =E∥xt− 1 2 − ˆxt− 1 − C (xt− 1 2 − ˆxt− 1) + xt − xt− 1 2 ∥2 F ≤ (1 + α 5)

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Compressed Momentum-based Single-Point Zeroth-Order Algorithm for Stochastic Distributed Nonconvex Optimization

math.OC · 2025-12-06 · unverdicted · novelty 3.0

The algorithm converges exactly to a stationary point with diminishing steps and reaches a neighborhood at sublinear rate with fixed steps under stochastic zeroth-order information and compression.

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Compressed Momentum-based Single-Point Zeroth-Order Algorithm for Stochastic Distributed Nonconvex Optimization math.OC · 2025-12-06 · unverdicted · none · ref 3
The algorithm converges exactly to a stationary point with diminishing steps and reaches a neighborhood at sublinear rate with fixed steps under stochastic zeroth-order information and compression.

(37) (i) Now, we provide the upper bound of E∥xt − xt− 1 2 ∥2 F

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