DREAM: Delay-Resistant Acceleration with Momentum
Abstract
With exact, delay-free gradients, Nesterov's accelerated gradient (NAG) achieves optimal √κ dependence for L-smooth, μ-strongly convex objectives, where κ=L/μ; heavy-ball (HB) achieves the same scaling on strongly convex quadratics. In asynchronous and distributed settings, gradients can be inexact, with delays varying across workers and iterations. We isolate staleness using a fixed delay τ≥1, replacing ∇ f(yk) with ∇ f(yk−τ) at iteration k. Arjevani, Shamir, and Srebro establish a worst-case lower bound of Ω(τ√κlog(1/ε)) iterations to reach objective error at most ε as ε→0. We show that for any fixed positive delay, neither NAG nor HB retains √κ-acceleration on strongly convex quadratics when updating every iteration, for any stable constant step size and positive momentum. We introduce delay-resistant accelerated momentum (DREAM), which decouples gradient-query extrapolation from momentum and uses explicit delay-dependent parameters. DREAM attains a linear convergence rate 1−Θ(1/(τ√κ)) for all smooth strongly convex objectives as κ→∞, yielding complexity matching the delayed first-order lower bound up to logarithmic factors. Our proof combines characteristic-polynomial stability analysis on quadratics with an analytic Zames--Falb integral quadratic constraint certificate. We extend DREAM to smooth convex objectives, obtaining near-optimal iteration complexity up to logarithmic factors for sufficiently small target accuracy. Experiments on strongly convex quadratics and regularized logistic regression corroborate DREAM's accelerated condition-number dependence under delay, unlike NAG and HB, and suggest this scaling persists when parameters use a conservative bound on the true delay.
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BibTeX
@misc{gurbuzbalaban2026dream,
title = {{DREAM: Delay-Resistant Acceleration with Momentum}},
author = {Mert Gürbüzbalaban and M. Hamza Rafi and Necdet Serhat Aybat and Waheed U. Bajwa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37444},
eprint = {2610.37444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37444},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DREAM: Delay-Resistant Acceleration with Momentum
AU - Mert Gürbüzbalaban
AU - M. Hamza Rafi
AU - Necdet Serhat Aybat
AU - Waheed U. Bajwa
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37444
UR - https://arxiv.org/abs/2610.37444
AB - With exact, delay-free gradients, Nesterov's accelerated gradient (NAG) achieves optimal √κ dependence for L-smooth, μ-strongly convex objectives, where κ=L/μ; heavy-ball (HB) achieves the same scaling on strongly convex quadratics. In asynchronous and distributed settings, gradients can be inexact, with delays varying across workers and iterations. We isolate staleness using a fixed delay τ≥1, replacing ∇ f(y_k) with ∇ f(y_k−τ) at iteration k. Arjevani, Shamir, and Srebro establish a worst-case lower bound of Ω(τ√κlog(1/ε)) iterations to reach objective error at most ε as ε→0. We show that for any fixed positive delay, neither NAG nor HB retains √κ-acceleration on strongly convex quadratics when updating every iteration, for any stable constant step size and positive momentum. We introduce delay-resistant accelerated momentum (DREAM), which decouples gradient-query extrapolation from momentum and uses explicit delay-dependent parameters. DREAM attains a linear convergence rate 1−Θ(1/(τ√κ)) for all smooth strongly convex objectives as κ→∞, yielding complexity matching the delayed first-order lower bound up to logarithmic factors. Our proof combines characteristic-polynomial stability analysis on quadratics with an analytic Zames--Falb integral quadratic constraint certificate. We extend DREAM to smooth convex objectives, obtaining near-optimal iteration complexity up to logarithmic factors for sufficiently small target accuracy. Experiments on strongly convex quadratics and regularized logistic regression corroborate DREAM's accelerated condition-number dependence under delay, unlike NAG and HB, and suggest this scaling persists when parameters use a conservative bound on the true delay.
ER -