{
  "abstract": "Primal-dual methods for constrained Markov decision processes are analyzed under a two-timescale assumption, with non-stationarity entering through two channels. In the additive channel, where the constraint level oscillates, the dual oscillation saturates at a floor set by the moving optimum and is amplified linearly by the timescale ratio. In the parametric channel, where the constraint sensitivity oscillates, a coherent modulation carries no resonant forcing at any depth: the dual update's stiffness modulation cancels the primal update's damping modulation. Instability instead comes from a mismatch between the constraint estimate used by the primal update and the measurement used by the dual update, producing a parametric resonance at twice the pair's natural frequency. The tolerated mismatch grows with the square root of the forcing bandwidth and collapses with the square root of the dual-to-primal step-size ratio. These results hold on the tangent linear-quadratic reduction around an active saddle, for one constraint and for $K$ constraints under a common modulation and an isotropy condition. Driving both updates from the same estimate removes the resonant forcing but introduces a stationary offset equal to the estimator's bias. In a Lagrangian soft actor-critic agent, the multiplier locks onto the sub-harmonic at the timescale ratios its identified linear loop predicts and a coherent cost critic suppresses the lock-in, while a proportional (PID) term, predicted to leave the lock-in in place, suppresses most of it through the projection of the multiplier.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23788",
  "author_total": 1,
  "authors": [
    {
      "name": "Maxime Baelde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mkfbk2x5m1df.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23788",
  "fulltext_url": null,
  "id": "3mkfbk2x5m1df",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23788",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7222933462",
  "pdf_url": "https://arxiv.org/pdf/2610.23788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mkfbk2x5m1df.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Parametric Resonance in Primal-Dual Learning for Slowly Non-Stationary Constrained MDPs",
  "title_text": "Parametric Resonance in Primal-Dual Learning for Slowly Non-Stationary Constrained MDPs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/3mkfbk2x5m1df",
  "venue": "arXiv",
  "versions": []
}