{
  "id": "1805.11454",
  "version": "v1",
  "published": "2018-05-25T23:34:48.000Z",
  "updated": "2018-05-25T23:34:48.000Z",
  "title": "Distributed Stochastic Gradient Tracking Methods",
  "authors": [
    "Shi Pu",
    "Angelia Nedić"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1803.07741",
  "categories": [
    "math.OC",
    "cs.DC",
    "cs.SI",
    "stat.ML"
  ],
  "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 (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). 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 stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size $n$, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T23:34:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributed stochastic gradient tracking method",
      "local cost function",
      "gsgt incurs lower communication cost"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}