{
  "id": "1803.07741",
  "version": "v1",
  "published": "2018-03-21T04:05:25.000Z",
  "updated": "2018-03-21T04:05:25.000Z",
  "title": "A Distributed Stochastic Gradient Tracking Method",
  "authors": [
    "Shi Pu",
    "Angelia Nedić"
  ],
  "categories": [
    "math.OC",
    "cs.DC",
    "cs.MA"
  ],
  "abstract": "In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-21T04:05:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributed stochastic gradient tracking method",
      "local cost function",
      "constant step size choice",
      "optimal solution decrease",
      "centralized stochastic gradient algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}