{
  "id": "2006.10815",
  "version": "v1",
  "published": "2020-06-18T19:11:54.000Z",
  "updated": "2020-06-18T19:11:54.000Z",
  "title": "Automatically Learning Compact Quality-aware Surrogates for Optimization Problems",
  "authors": [
    "Kai Wang",
    "Bryan Wilder",
    "Andrew Perrault",
    "Milind Tambe"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space. Empirically, we demonstrate these improvements on a non-convex adversary modeling task, a submodular recommendation task and a convex portfolio optimization task.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-18T19:11:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automatically learning compact quality-aware surrogates",
      "optimization problem",
      "low-dimensional surrogate model end-to-end",
      "unknown parameters",
      "convex portfolio optimization task"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}