{
  "abstract": "We study online vector balancing with $N$ random vectors in $\\mathbb{R}^M$ revealed sequentially, where each vector must be assigned an irrevocable sign upon arrival. The goal is to minimize the expected $\\ell^\\infty$ norm of the final signed sum. For i.i.d. entries with mean zero, variance one, and a finite fourth moment, we prove that, as $M/N\\toα\\in(0,\\infty)$, the optimal value divided by $\\sqrt N$ converges to a limit $R_α$ independent of the entry distribution. This limit is the stochastic control value identified for Gaussian inputs by Fiedler, Jackson, Lacker, and Niles-Weed. In particular, it determines the exact asymptotic optimum for Rademacher inputs. For every $κ>R_α$, we construct a randomized online algorithm whose final signed sum has $\\ell^\\infty$ norm at most $κ\\sqrt N$ with high probability; for $κ<R_α$, every online algorithm has vanishing success probability. Consequently, the online threshold of the symmetric binary perceptron is universal at every positive margin. The main step is a coupling that transfers Brownian controls to non-Gaussian inputs, while truncation controls rare large entries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00103",
  "author_total": 2,
  "authors": [
    {
      "name": "Sunghyeon Jo"
    },
    {
      "name": "Taekyun Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ratrvs589x7h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00103",
  "fulltext_url": null,
  "id": "8ratrvs589x7h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00103",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7216042543",
  "pdf_url": "https://arxiv.org/pdf/2610.00103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ratrvs589x7h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Exact Universality of Online Discrepancy",
  "title_text": "Exact Universality of Online Discrepancy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8ratrvs589x7h",
  "venue": "arXiv",
  "versions": []
}