{
  "abstract": "We study finite-horizon LQR with independent disturbances whose laws may drift over time. We address uncertainty in this evolution through ex-ante distributionally robust regret optimization (DRRO), which minimizes worst-case excess expected cost relative to the optimal causal controller that knows the law sequence. To specify the admissible law sequences, we introduce a temporally coupled moment ambiguity set with a Gelbrich kinetic-energy budget and a second budget limiting departures from reference moments and persistent cumulative mismatch. Despite the coupling of moments across time, affine disturbance-feedback synthesis reduces exactly to a semidefinite program. An optimal policy uses past disturbances to predict the correction to nominal LQR determined by current and future disturbance means. The SDP solution also yields worst-case moment paths and corresponding laws. For standard distributionally robust optimization (DRO), the analogous SDP relaxation can have a duality gap. Portfolio liquidation experiments show substantially lower worst-case regret over the drifting ambiguity set than common-law DRRO and nominal control.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09220",
  "author_total": 2,
  "authors": [
    {
      "name": "Lukas-Benedikt Fiechtner"
    },
    {
      "name": "Jose Blanchet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85e3wscdkvn8d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09220",
  "fulltext_url": null,
  "id": "85e3wscdkvn8d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09220",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7220968533",
  "pdf_url": "https://arxiv.org/pdf/2610.09220",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85e3wscdkvn8d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09220",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09220"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Regret-Optimal Linear-Quadratic Control under Distributional Drift",
  "title_text": "Regret-Optimal Linear-Quadratic Control under Distributional Drift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/85e3wscdkvn8d",
  "venue": "arXiv",
  "versions": []
}