{
  "id": "2210.15576",
  "version": "v1",
  "published": "2022-10-27T16:13:48.000Z",
  "updated": "2022-10-27T16:13:48.000Z",
  "title": "Regret Bounds and Experimental Design for Estimate-then-Optimize",
  "authors": [
    "Samuel Tan",
    "Peter I. Frazier"
  ],
  "categories": [
    "math.OC",
    "stat.ML"
  ],
  "abstract": "In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to optimize the structural model's predicted outcome as if its parameters were correctly estimated. Due to its flexibility and simple implementation, this ``estimate-then-optimize'' approach is often used for data-driven decision-making. Errors in the estimation step can lead estimate-then-optimize to sub-optimal decisions that result in regret, i.e., a difference in value between the decision made and the best decision available with knowledge of the structural model's parameters. We provide a novel bound on this regret for smooth and unconstrained optimization problems. Using this bound, in settings where estimated parameters are linear transformations of sub-Gaussian random vectors, we provide a general procedure for experimental design to minimize the regret resulting from estimate-then-optimize. We demonstrate our approach on simple examples and a pandemic control application.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-27T16:13:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "experimental design",
      "regret bounds",
      "estimate-then-optimize",
      "machine learning model estimates parameters",
      "structural model relating decisions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}