### Abstract

In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization of the primal and dual variables, both algorithms are able to compute second-order stationary solutions (ss2) with probability one. This is the first result showing that primal-dual algorithm is capable of finding ss2 when only using first-order information; it also extends the existing results for first-order, but primal-only algorithms. An important implication of our result is that it also gives rise to the first global convergence result to the ss2, for two classes of unconstrained distributed non-convex learning problems over multi-agent networks.

Original language | English (US) |
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Title of host publication | 35th International Conference on Machine Learning, ICML 2018 |

Editors | Jennifer Dy, Andreas Krause |

Publisher | International Machine Learning Society (IMLS) |

Pages | 3189-3198 |

Number of pages | 10 |

ISBN (Electronic) | 9781510867963 |

State | Published - Jan 1 2018 |

Externally published | Yes |

Event | 35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden Duration: Jul 10 2018 → Jul 15 2018 |

### Publication series

Name | 35th International Conference on Machine Learning, ICML 2018 |
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Volume | 5 |

### Other

Other | 35th International Conference on Machine Learning, ICML 2018 |
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Country | Sweden |

City | Stockholm |

Period | 7/10/18 → 7/15/18 |

### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Human-Computer Interaction
- Software

## Cite this

*35th International Conference on Machine Learning, ICML 2018*(pp. 3189-3198). (35th International Conference on Machine Learning, ICML 2018; Vol. 5). International Machine Learning Society (IMLS).