## Abstract

We consider solving a convex optimization problem with possibly stochastic gradient, and over a randomly time-varying multiagent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the smooth component. We develop a dynamic stochastic proximal-gradient consensus algorithm, with the following key features: 1) it works for both the static and certain randomly time-varying networks; 2) it allows the agents to utilize either the exact or stochastic gradient information; 3) it is convergent with provable rate. In particular, the proposed algorithm converges to a global optimal solution, with a rate of \mathcal O(1/r) [resp. \mathcal O(1/r) when the exact (resp. stochastic) gradient is available, where r is the iteration counter. Interestingly, the developed algorithm establishes a close connection among a number of (seemingly unrelated) distributed algorithms, such as the EXTRA, the PG-EXTRA, the IC/IDC-ADMM, the DLM, and the classical distributed subgradient method.

Original language | English (US) |
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Article number | 7862886 |

Pages (from-to) | 2933-2948 |

Number of pages | 16 |

Journal | IEEE Transactions on Signal Processing |

Volume | 65 |

Issue number | 11 |

DOIs | |

State | Published - Jun 1 2017 |

### Bibliographical note

Funding Information:The work of M. Hong was supported in part by the National Science Foundation under Grant CCF-1526078 and in part by Air Force Office of Scientific Research under Grant 15RT0767. The work of T.-H. Chang was supported by the National Natural Science Foundation of China, under Grant 61571385.

Publisher Copyright:

© 2017 IEEE.

## Keywords

- ADMM
- Distributed optimization
- fast algorithms
- rate analysis