{
  "abstract": "We analyze a stochastic algorithm with Halpern-type anchoring for constrained convex-concave problems and monotone variational inequalities. This single-loop and single-call algorithm uses one unbiased sample of the gradient operator at every iteration, to be applicable to monotone games with noisy feedback. With $t$ denoting the iteration counter, we prove an anytime last-iterate convergence rate of $O(t^{-1/4})$ for both the gradient-mapping norm and restricted gap, bypassing the $O(t^{-1/5})$ constrained-anytime bottleneck in the literature. Specializing then to multi-point oracles, we use variance reduction to achieve the $O(t^{-1/2})$ rate with an anytime single-loop algorithm using $2$ samples per iteration. Our results allow constrained problems with a potentially unbounded feasible set; as well as a structured class of stochastic oracles whose variance need not be uniformly bounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15257",
  "author_total": 2,
  "authors": [
    {
      "name": "Jun-Hyun Kim"
    },
    {
      "name": "Ahmet Alacaoglu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cxkd5xsvs7w2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15257",
  "fulltext_url": null,
  "id": "3cxkd5xsvs7w2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15257",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7213267368",
  "pdf_url": "https://arxiv.org/pdf/2609.15257",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cxkd5xsvs7w2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.15257",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15257"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities",
  "title_text": "Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3cxkd5xsvs7w2",
  "venue": "arXiv",
  "versions": []
}