{
  "abstract": "We study online convex optimization on a bounded Euclidean domain when the learner receives only one subgradient at its prediction and knows neither the horizon, a gradient bound, nor the losses' strong-convexity parameters. We present a scale-invariant algorithm that couples projected adaptive gradient descent to one cone-constrained quadratic leader through a positive wealth process. The algorithm maintains $O(d)$ state, without a learning-rate grid or restarts. For a domain of diameter at most $D$, it guarantees regret at most $\\sqrt{2}D(\\sum_t\\|\\widehat g_t\\|^2)^{1/2}+2D\\max_t\\|\\widehat g_t\\|$, with no logarithmic factor. A simultaneous quadratic-distance bound yields explicit improvements for unknown strong convexity, including a refinement governed by jumps in the observed gradient scale. For varying per-round curvature, the bound depends on the total shortfall below a reference level selected in hindsight. The proof uses a clipping-compatible surrogate and a potential involving the quadratic minimum, log wealth, and two scalar curvature statistics. The resulting strongly convex bound is not uniform at the classical logarithmic rate over all curvature-to-gradient ratios; the exact parameter dependence is stated. The contribution is a single-leader construction and its analysis, within an established literature on universal and scale-free online learning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00190",
  "author_total": 1,
  "authors": [
    {
      "name": "Kamiar Asgari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ds8249sgn3baq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00190",
  "fulltext_url": null,
  "id": "ds8249sgn3baq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00190",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7216105115",
  "pdf_url": "https://arxiv.org/pdf/2610.00190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ds8249sgn3baq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.00190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00190"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Gradient-Only Online Convex Optimization with a Single Quadratic Leader",
  "title_text": "Gradient-Only Online Convex Optimization with a Single Quadratic Leader",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/ds8249sgn3baq",
  "venue": "arXiv",
  "versions": []
}