{
  "id": "1405.3229",
  "version": "v1",
  "published": "2014-05-13T16:51:54.000Z",
  "updated": "2014-05-13T16:51:54.000Z",
  "title": "Rate of Convergence and Error Bounds for LSTD($λ$)",
  "authors": [
    "Manel Tagorti",
    "Bruno Scherrer"
  ],
  "comment": "(2014)",
  "categories": [
    "cs.LG",
    "cs.AI",
    "math.OC",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We consider LSTD($\\lambda$), the least-squares temporal-difference algorithm with eligibility traces algorithm proposed by Boyan (2002). It computes a linear approximation of the value function of a fixed policy in a large Markov Decision Process. Under a $\\beta$-mixing assumption, we derive, for any value of $\\lambda \\in (0,1)$, a high-probability estimate of the rate of convergence of this algorithm to its limit. We deduce a high-probability bound on the error of this algorithm, that extends (and slightly improves) that derived by Lazaric et al. (2012) in the specific case where $\\lambda=0$. In particular, our analysis sheds some light on the choice of $\\lambda$ with respect to the quality of the chosen linear space and the number of samples, that complies with simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-13T16:51:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "error bounds",
      "convergence",
      "large markov decision process",
      "eligibility traces algorithm",
      "least-squares temporal-difference algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3229T"
    }
  }
}