{
  "abstract": "Among distinct optimal acceleration mechanisms for deterministic monotone root-finding problems and fixed-point problems, dual-anchoring has recently been shown to admit a more robust direct stochastic extension than standard anchor acceleration. However, without additional strong monotonicity, the existing stochastic dual-anchoring guarantee has two limitations: first, it requires cocoercivity in expectation, and second, it attains only $O(ε^{-3})$ oracle complexity, leaving a gap to the near-optimal $\\tilde{O}(ε^{-2})$ complexity achieved by other methods. In this work, we address both of these limitations by combining dual-anchoring with stochastic resolvent approximation and optimized variance control. For unbiased stochastic oracles with variance bounded by $σ^2$, where sample operators are monotone and uniformly $L$-Lipschitz, our algorithm finds a point with $ε$-residual with a near-optimal oracle complexity of $O ( (LD / ε) \\ell + (σ^2 / ε^2) \\ell^2)$, where $\\ell = \\log (1 + LD / ε)$ and $D$ is the initial distance to a solution. This result improves the best known oracle complexity in the noise-dominated regime under these samplewise assumptions, reducing the poly-logarithmic factor from cubic to quadratic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36033",
  "author_total": 2,
  "authors": [
    {
      "name": "TaeHo Yoon"
    },
    {
      "name": "Nicolas Loizou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58ctrdtj2ms8x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36033",
  "fulltext_url": null,
  "id": "58ctrdtj2ms8x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36033",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214905250",
  "pdf_url": "https://arxiv.org/pdf/2609.36033",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58ctrdtj2ms8x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36033",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36033"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding",
  "title_text": "Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/58ctrdtj2ms8x",
  "venue": "arXiv",
  "versions": []
}