{
  "abstract": "The explore-exploit trade-off is the core problem of reinforcement learning (RL). In its multi-agent, resource-sharing form the optimum is not a scalar-return maximum but an equilibrium allocation -- the ideal-free distribution (IFD), the Nash equilibrium of a congestion game. We show that a minimal foraging swarm reaches the shape of this equilibrium as a self-organized attractor -- foragers in proportion to resource richness (matching slope 0.94) -- with no learner, no trained parameters, and no payoff or reward read anywhere in its dynamics. Agents explore by heavy-tailed (Levy) flights, recruit neighbours to a discovery through a threshold cascade on their proximity network, and disperse as a patch crowds; removing the coupling of recruitment to movement collapses the matching (slope 0.08). The reinforcement learning is at the level of the problem and the allocation reached, not the micro-rule. The swarm reaches this equilibrium rather than learning it, attaining its shape but not the exact equilibrium: it stays measurably exploitable (Nash-gap 0.58 versus ~0.01 for a converged learner). Against PPO learners (feedforward, centralized-critic, and graph message-passing) trained in the same sensing-limited environment, the reward-free swarm at zero training matches the IFD gradient more faithfully than any learner (slope ~1 vs 0.69-0.91) and ties the best learner's harvest where clustered (both plateau at ~0.80 of an oracle ceiling), while the learner collects more where resource is scarce (0.33 vs 0.22) and holds tighter per-capita intake. Learning thus buys precision and transfer, not a better allocation; neither message passing nor a centralized critic exceeds it at this budget. We read this not as beating RL, but as evidence that a minimal swarm's physics reaches the equilibrium RL seeks without a learner, a reward, or a trained parameter. A companion paper develops the mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25113",
  "author_total": 1,
  "authors": [
    {
      "name": "Galen J. Wilkerson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tj91rt6gwhaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25113",
  "fulltext_url": null,
  "id": "3tj91rt6gwhaz",
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  "landing_url": "https://arxiv.org/abs/2610.25113",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
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      "cs.SI"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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      "arxiv",
      "nlin.AO"
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      "arxiv",
      "physics.bio-ph"
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      "openalex",
      "1702|Reinforcement Learning in Robotics"
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  "openalex": "W7223053946",
  "pdf_url": "https://arxiv.org/pdf/2610.25113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tj91rt6gwhaz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.25113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A learner-free swarm reaches the explore-exploit equilibrium: A self-organized attractor approximating the reinforcement-learning solution",
  "title_text": "A learner-free swarm reaches the explore-exploit equilibrium: A self-organized attractor approximating the reinforcement-learning solution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3tj91rt6gwhaz",
  "venue": "arXiv",
  "versions": []
}