### Abstract

In this paper, we study a problem of learning a linear regression model distributively with a network of N interconnected agents in which each agent can deploy an online learning algorithm to adaptively learn the regression model using its private data. The goal of the problem is to devise a distributed algorithm, under the constraint that each agent can communicate only with its neighbors depicted by a connected communication graph, which enables all N agents converge to the true model, with a performance comparable to that of conventional centralized algorithms. We propose a differentially private distributed algorithm, called private gossi» gradient descent, and establish E-differential privacy and Oleft(sqrt{frac{log {2}t}{epsilon(1-lambda-{2})Nt}}right) convergence, where A2 is the second largest eigenvalue of the expected gossip matrix corresponding to the communication graph.

Original language | English (US) |
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Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2777-2782 |

Number of pages | 6 |

ISBN (Electronic) | 9781538613955 |

DOIs | |

State | Published - Jan 18 2019 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2018-December |

ISSN (Print) | 0743-1546 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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Country | United States |

City | Miami |

Period | 12/17/18 → 12/19/18 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*2018 IEEE Conference on Decision and Control, CDC 2018*(pp. 2777-2782). [8619437] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619437