{
  "id": "2210.08886",
  "version": "v1",
  "published": "2022-10-17T09:29:01.000Z",
  "updated": "2022-10-17T09:29:01.000Z",
  "title": "Regret Bounds for Learning Decentralized Linear Quadratic Regulator with Partially Nested Information Structure",
  "authors": [
    "Lintao Ye",
    "Ming Chi",
    "Vijay Gupta"
  ],
  "categories": [
    "math.OC",
    "cs.LG",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "We study the problem of learning decentralized linear quadratic regulator under a partially nested information constraint, when the system model is unknown a priori. We propose an online learning algorithm that adaptively designs a control policy as new data samples from a single system trajectory become available. Our algorithm design uses a disturbance-feedback representation of state-feedback controllers coupled with online convex optimization with memory and delayed feedback. We show that our online algorithm yields a controller that satisfies the desired information constraint and enjoys an expected regret that scales as $\\sqrt{T}$ with the time horizon $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T09:29:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "learning decentralized linear quadratic regulator",
      "partially nested information structure",
      "regret bounds",
      "information constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}