{
  "abstract": "We study online task assignment with reusable resources. This problem arises in peer reviewer assignment, skill-based call routing, rideshare matching, emergency dispatch, and crowdsourcing: Tasks arrive according to a geometric process and must be immediately assigned to servers that become temporarily busy, yielding rewards that depend on the task-server pair. The goal is to maximize long-run average reward. We cast the problem as a contextual restless multi-armed bandit (CRMAB). We derive an occupancy-measure LP (OCC-LP) that upper-bounds the reward of any work-conserving policy. From its dual we obtain Lag, a closed-form index policy. We introduce a scaling regime in which the number of copies of each server and the number of arrivals per step grow together. This regime yields the first deterministic fluid limit for a contextual bandit. In it, Lag is asymptotically optimal. Finally, we evaluate our algorithms on peer review datasets and call center routing. The Lagrangian index achieves 83-99% of the LP upper bound across all load levels. Moreover, the Lagrangian index policy significantly outperforms the natural greedy assignment scheme, improving reward by up to 12.3% on journal data and 36% on structured synthetic instances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19038",
  "author_total": 1,
  "authors": [
    {
      "name": "Keerthana Gurushankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y48jzwh9hfpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19038",
  "fulltext_url": null,
  "id": "9y48jzwh9hfpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19038",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.PF"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7222066376",
  "pdf_url": "https://arxiv.org/pdf/2610.19038",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y48jzwh9hfpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19038",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19038"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Lag: A Mean-Field Optimal Policy for Online Assignment with Reusable Resources",
  "title_text": "Lag: A Mean-Field Optimal Policy for Online Assignment with Reusable Resources",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/9y48jzwh9hfpc",
  "venue": "arXiv",
  "versions": []
}