{
  "abstract": "In online inverse linear optimization, the learner predicts a weight at each round, observes the optimal action of the agent, and updates its prediction. In the general setting, the gap of $\\log T$ between the regret upper bound $O(d \\log T)$ and the lower bound $Ω(d)$ is unresolved (here $T$ is the total number of rounds and $d$ is the dimension). When the action set is M-convex, the regret is known to be bounded by $O(d \\log d)$, but the method attaining it computes a center of gravity at every round. This paper therefore proposes Small-Gradient Skipping (SGS), a mechanism that skips the update at rounds without a mistake, and applies it to online gradient descent, the online Newton step, and MetaGrad. When the forward problem is an integer linear program with a unique optimal solution, the number of mistakes is bounded, for all three, by a quantity independent of $T$; and for the online Newton step and for MetaGrad with SGS, the dimension dependence of the regret becomes $O(d^2)$, that is, the factor $\\log T$ is removed. Moreover, when the action set is M-convex, the regret is bounded efficiently without computing a center of gravity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09809",
  "author_total": 1,
  "authors": [
    {
      "name": "Akira Kitaoka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2a3b4v90s0frj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09809",
  "fulltext_url": null,
  "id": "2a3b4v90s0frj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09809",
  "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.DS"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7212115421",
  "pdf_url": "https://arxiv.org/pdf/2609.09809",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2a3b4v90s0frj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.09809",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09809"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Online Inverse Integer Linear Optimization via Small-Gradient Skipping: Constant Regret and Finite Mistakes",
  "title_text": "Online Inverse Integer Linear Optimization via Small-Gradient Skipping: Constant Regret and Finite Mistakes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2a3b4v90s0frj",
  "venue": "arXiv",
  "versions": []
}