{
  "abstract": "We study how predefined randomized parameter schedules accelerate the heavy-ball method on general smooth convex objectives. Our analysis distinguishes two levels of randomization: sampling gradient-evaluation times within intervals whose boundaries are deterministic, and additionally randomizing the time boundaries themselves. With deterministic time boundaries, we construct fixed-time and anytime schedules that achieve an expected last-iterate function value gap of order $\\mathcal{O}(1/K^{4/3})$; the anytime schedule also satisfies the same rate almost surely. We then use randomized time boundaries and obtain the improved last-iterate rate $\\mathcal{O}(1/K^{3/2})$, both in expectation and almost surely. To the best of our knowledge, this is the first global nonasymptotic convergence guarantee for the heavy-ball method on general smooth convex functions that improves polynomially over the classical $\\mathcal{O}(1/K)$ rate. Our result shows that the heavy-ball method achieves a strictly better convergence rate than the best known result $\\mathcal{O}(1/K^{\\log_2(1+\\sqrt{2})})$ attainable by plain gradient descent with silver stepsize schedules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09743",
  "author_total": 2,
  "authors": [
    {
      "name": "Chang He"
    },
    {
      "name": "Shuzhong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/114mp7876shq9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09743",
  "fulltext_url": null,
  "id": "114mp7876shq9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09743",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7212165676",
  "pdf_url": "https://arxiv.org/pdf/2609.09743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/114mp7876shq9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09743"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Heavy-Ball Method under Randomized Schedules",
  "title_text": "Heavy-Ball Method under Randomized Schedules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/114mp7876shq9",
  "venue": "arXiv",
  "versions": []
}