{
  "id": "2109.06343",
  "version": "v1",
  "published": "2021-09-13T21:57:34.000Z",
  "updated": "2021-09-13T21:57:34.000Z",
  "title": "Data-based Online Optimization of Networked Systems with Infrequent Feedback",
  "authors": [
    "Ana M. Ospina",
    "Nicola Bastianello",
    "Emiliano Dall'Anese"
  ],
  "comment": "Submitted to IEEE L-CSS and ACC 2022",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "We consider optimization problems for (networked) systems, where we minimize a cost that includes a known time-varying function associated with the system's outputs and an unknown function of the inputs. We focus on a data-based online projected gradient algorithm where: i) the input-output map of the system is replaced by measurements of the output whenever available (thus leading to a \"closed-loop\" setup); and ii) the unknown function is learned based on functional evaluations that may occur infrequently. Accordingly, the feedback-based online algorithm operates in a regime with inexact gradient knowledge and with random updates. We show that the online algorithm generates points that are within a bounded error from the optimal solution of the problem; in particular, we provide error bounds in expectation and in high-probability, where the latter is given when the gradient error follows a sub-Weibull distribution and when missing measurements are modeled as Bernoulli random variables. We also provide results in terms of input-to-state stability in expectation and in probability. Numerical results are presented in the context of a demand response task in power systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-13T21:57:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "data-based online optimization",
      "infrequent feedback",
      "networked systems",
      "online algorithm generates points",
      "unknown function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}