{
  "abstract": "Variance reduction is indispensable in Byzantine-resilient decentralized stochastic optimization over multi-agent systems (MASs), as it effectively mitigates gradient noise to facilitate the resilient aggregation process. However, most existing Byzantine-resilient decentralized variance-reduced (VR) stochastic gradient algorithms rely on random data sampling, which proves inefficient in data-scarce yet high-dimensional tasks, for instance, image deblurring. This paper aims to pursue an alternative approach that achieves variance reduction via gradient sketching. We first formulate a class of structural risk minimization (SRM) problems over time-varying networks, where the local objectives are not necessarily decomposable and their gradients may be inaccessible. To solve the SRM problems in a decentralized manner, we incorporate a localized gradient-sketching technique into a preconditioned stochastic proximal gradient framework, proposing a novel gossip-based decentralized algorithm with variance reduction, dubbed Gossip-SEGA. To further enhance its resilience, we substitute the weighted-average aggregation in Gossip-SEGA with a norm-penalized approximation, thereby developing a Byzantine-resilient decentralized algorithm, namely RED-SEGA. Theoretically, we derive sufficient conditions for both consensus among reliable agents and (sub)linear convergence rate of RED-SEGA over time-varying networks in the presence of Byzantine agents with unknown identities. This is challenging, as the convergence and consensus errors must be bounded within a transformed variable-metric geometry, where the inherent complexities are further compounded by adversarial Byzantine agents and time-varying networks. The effectiveness and resilience of RED-SEGA are validated by solving a constrained least-squares problem and an image deblurring task under various Byzantine attacks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10791",
  "author_total": 5,
  "authors": [
    {
      "name": "Jinhui Hu"
    },
    {
      "name": "Guo Chen"
    },
    {
      "name": "Huaqing Li"
    },
    {
      "name": "Tao Han"
    },
    {
      "name": "Tingwen Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59j8bjk4jx8v6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10791",
  "fulltext_url": null,
  "id": "59j8bjk4jx8v6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10791",
  "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",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7168292173",
  "pdf_url": "https://arxiv.org/pdf/2607.10791",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/59j8bjk4jx8v6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2607.10791",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10791"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Resilient Decentralized Preconditioned Stochastic Proximal Optimization with Gradient Sketching over Time-Varying Networks",
  "title_text": "Resilient Decentralized Preconditioned Stochastic Proximal Optimization with Gradient Sketching over Time-Varying Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/59j8bjk4jx8v6",
  "venue": "arXiv",
  "versions": []
}