{
  "abstract": "We study online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube. The best known constructive offline approximation factor is $0.401$ under the corresponding meta-solvability assumptions, whereas comparable adversarial online guarantees had remained at $1/e$. We show that this factor is also achievable online. In the post-decision full-information value-oracle model, our algorithm attains factor $0.401$ with sublinear approximate regret when oracle feedback is conditionally unbiased and bounded. The online algorithm does not run the offline construction on a changing objective. Instead, it replaces the offline objective-dependent box step by a weighted online learner that controls the required residual terms cumulatively. An exact asymmetric balance theorem preserves the offline coefficients despite adversarial variation. The direct implementation has $O(T^{3/4})$ regret and uses $O(dT^{1/4})$ oracle calls per round. More generally, for every $δ\\in[0,1/4]$, batching gives $O(T^δ)$ calls per round and $O(T^{4/5-δ/5})$ regret, including a one-call $O(T^{4/5})$ endpoint. Under a positive-anchor condition, randomized blocking retains factor $0.401$ with $O(T^{5/6})$ one-point bandit regret.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02145",
  "author_total": 2,
  "authors": [
    {
      "name": "Vaneet Aggarwal"
    },
    {
      "name": "Yiyang Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nhedyjh1kjzs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02145",
  "fulltext_url": null,
  "id": "5nhedyjh1kjzs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02145",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7207801832",
  "pdf_url": "https://arxiv.org/pdf/2609.02145",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nhedyjh1kjzs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:26Z",
      "native_id": "2609.02145",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02145"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Online Non-Monotone DR-Submodular Maximization Matching the Offline $0.401$ Factor",
  "title_text": "Online Non-Monotone DR-Submodular Maximization Matching the Offline $0.401$ Factor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:26Z",
  "url": "https://research.draconitic.com/paper/5nhedyjh1kjzs",
  "venue": "arXiv",
  "versions": []
}