{
  "abstract": "KL geometry accelerates restart schedules in stochastic weakly-convex optimization, but the schedule depends jointly on an unknown and potentially nonunique geometric description. We introduce CARP-KL, a certified portfolio that adapts over valid KL descriptions while using the same primitive stochastic-subgradient oracle for both optimization and candidate selection. Over declared polynomial parameter ranges, CARP-KL competes with every affordable valid description and preserves the known-description polynomial Moreau-stationarity rate up to logarithmic factors, without objective values, an exact proximal map, direct Moreau-gradient access, or a bounded-domain assumption. Controlled experiments quantify the finite-budget price of this universality. The portfolio repeatedly contains strong candidates, while certification consumes a substantial share of the oracle budget and finite-sample ranking limits their recovery. A common conservative gap bound further reduces the portfolio from $O(\\log^3 T)$ to $O(\\log^2 T)$ candidates with an explicit scale-mismatch penalty. The theory and diagnostics together establish certified unknown-geometry adaptation and pinpoint selection as the principal practical frontier of the current construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30650",
  "author_total": 3,
  "authors": [
    {
      "name": "Binh T. Nguyen"
    },
    {
      "name": "Khoa D. Nguyen"
    },
    {
      "name": "Bao Thai Huynh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efm9t39kjbabk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30650",
  "fulltext_url": null,
  "id": "efm9t39kjbabk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30650",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7223288354",
  "pdf_url": "https://arxiv.org/pdf/2610.30650",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efm9t39kjbabk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30650",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30650"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Adaptive Restart under Unknown KL Geometry in Stochastic Weakly-Convex Optimization",
  "title_text": "Adaptive Restart under Unknown KL Geometry in Stochastic Weakly-Convex Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/efm9t39kjbabk",
  "venue": "arXiv",
  "versions": []
}