{
  "id": "1802.09188",
  "version": "v1",
  "published": "2018-02-26T07:50:57.000Z",
  "updated": "2018-02-26T07:50:57.000Z",
  "title": "Analysis of Langevin Monte Carlo via convex optimization",
  "authors": [
    "Alain Durmus",
    "Szymon Majewski",
    "Błażej Miasojedow"
  ],
  "categories": [
    "stat.CO",
    "stat.ML"
  ],
  "abstract": "In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from logconcave smooth target distribution on $\\mathbb{R}^d$. Our proofs are then easily extended to the Stochastic Gradient Langevin Dynamics, which is a popular extension of the Unadjusted Langevin Algorithm. Finally, this interpretation leads to a new methodology to sample from a non-smooth target distribution, for which a similar study is done.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-26T07:50:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langevin monte carlo",
      "convex optimization",
      "unadjusted langevin algorithm",
      "stochastic gradient langevin dynamics",
      "first order optimization algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}