### Abstract

We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our algorithm to find an approximate local minimum is even faster than that of gradient descent to find a critical point. Our algorithm applies to a general class of optimization problems including training a neural network and other non-convex objectives arising in machine learning.

Original language | English (US) |
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Title of host publication | STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Pierre McKenzie, Valerie King, Hamed Hatami |

Publisher | Association for Computing Machinery |

Pages | 1195-1199 |

Number of pages | 5 |

ISBN (Electronic) | 9781450345286 |

DOIs | |

State | Published - Jun 19 2017 |

Event | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada Duration: Jun 19 2017 → Jun 23 2017 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F128415 |

ISSN (Print) | 0737-8017 |

### Other

Other | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 |
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Country | Canada |

City | Montreal |

Period | 6/19/17 → 6/23/17 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- Cubic regularization
- Deep learning
- Non-convex optimization
- Second-order optimization

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## Cite this

Agarwal, N., Allen-Zhu, Z., Bullins, B., Hazan, E., & Ma, T. (2017). Finding approximate local minima faster than gradient descent. In P. McKenzie, V. King, & H. Hatami (Eds.),

*STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing*(pp. 1195-1199). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F128415). Association for Computing Machinery. https://doi.org/10.1145/3055399.3055464