## Abstract

A key problem in a variety of applications is that of domain adaptation from a public source domain, for which a relatively large amount of labeled data with no privacy constraints is at one's disposal, to a private target domain, for which a private sample is available with very few or no labeled data. In regression problems, where there are no privacy constraints on the source or target data, a discrepancy minimization approach was shown to outperform a number of other adaptation algorithm baselines. Building on that approach, we initiate a principled study of differentially private adaptation from a source domain with public labeled data to a target domain with unlabeled private data. We design differentially private discrepancy-based adaptation algorithms for this problem. The design and analysis of our private algorithms critically hinge upon several key properties we prove for a smooth approximation of the weighted discrepancy, such as its smoothness with respect to the ℓ_{1}-norm and the sensitivity of its gradient. We formally show that our adaptation algorithms benefit from strong generalization and privacy guarantees.

Original language | English (US) |
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Pages (from-to) | 8405-8432 |

Number of pages | 28 |

Journal | Proceedings of Machine Learning Research |

Volume | 206 |

State | Published - 2023 |

Event | 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain Duration: Apr 25 2023 → Apr 27 2023 |

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability