{
  "abstract": "With exact, delay-free gradients, Nesterov's accelerated gradient (NAG) achieves optimal $\\sqrtκ$ 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 $τ\\ge1$, replacing $\\nabla f(y_k)$ with $\\nabla f(y_{k-τ})$ at iteration $k$. Arjevani, Shamir, and Srebro establish a worst-case lower bound of $Ω(τ\\sqrtκ\\log(1/\\varepsilon))$ iterations to reach objective error at most $\\varepsilon$ as $\\varepsilon\\to0$. We show that for any fixed positive delay, neither NAG nor HB retains $\\sqrtκ$-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 $1-Θ(1/(τ\\sqrtκ))$ for all smooth strongly convex objectives as $κ\\to\\infty$, 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37444",
  "author_total": 4,
  "authors": [
    {
      "name": "Mert Gürbüzbalaban"
    },
    {
      "name": "M. Hamza Rafi"
    },
    {
      "name": "Necdet Serhat Aybat"
    },
    {
      "name": "Waheed U. Bajwa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0e5ek0wp64wsz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37444",
  "fulltext_url": null,
  "id": "0e5ek0wp64wsz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37444",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7224117949",
  "pdf_url": "https://arxiv.org/pdf/2610.37444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0e5ek0wp64wsz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "DREAM: Delay-Resistant Acceleration with Momentum",
  "title_text": "DREAM: Delay-Resistant Acceleration with Momentum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/0e5ek0wp64wsz",
  "venue": "arXiv",
  "versions": []
}