### Abstract

We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can directly communicate with each other. This optimization model abstracts a number of applications in distributed sensing and machine learning. We show that any limit point of DFAL iterates is optimal; and for any ∈ > 0, an ∈-optimal and e-feasible solution can be computed within O(log(∈^{-1})) DFAL iterations, which require O(ψ^{1.5}_{max}/d_{m} ∈^{-1}) proximal gradient computations and communications per node in total, where ψ_{max} denotes the largest eigenvalue of the graph Laplacian, and d_{min} is the minimum degree of the graph. We also propose an asynchronous version of DFAL by incorporating randomized block coordinate descent methods; and demonstrate the efficiency of DFAL on large scale sparse-group LASSO problems.

Original language | English (US) |
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Title of host publication | 32nd International Conference on Machine Learning, ICML 2015 |

Editors | Francis Bach, David Blei |

Publisher | International Machine Learning Society (IMLS) |

Pages | 2444-2452 |

Number of pages | 9 |

Volume | 3 |

ISBN (Electronic) | 9781510810587 |

State | Published - Jan 1 2015 |

Event | 32nd International Conference on Machine Learning, ICML 2015 - Lile, France Duration: Jul 6 2015 → Jul 11 2015 |

### Other

Other | 32nd International Conference on Machine Learning, ICML 2015 |
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Country | France |

City | Lile |

Period | 7/6/15 → 7/11/15 |

### All Science Journal Classification (ASJC) codes

- Human-Computer Interaction
- Computer Science Applications

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## Cite this

*32nd International Conference on Machine Learning, ICML 2015*(Vol. 3, pp. 2444-2452). International Machine Learning Society (IMLS).