## Abstract

We introduce the concurrent shuffle model of differential privacy. In this model we have multiple concurrent shufflers permuting messages from different, possibly overlapping, batches of users. Similarly to the standard (single) shuffle model, the privacy requirement is that the concatenation of all shuffled messages should be differentially private. We study the private continual summation problem (a.k.a. the counter problem) and show that the concurrent shuffle model allows for significantly improved error compared to a standard (single) shuffle model. Specifically, we give a summation algorithm with error Õ(n^{1/(2k+1)}) with k concurrent shufflers on a sequence of length n. Furthermore, we prove that this bound is tight for any k, even if the algorithm can choose the sizes of the batches adaptively. For k = log n shufflers, the resulting error is polylogarithmic, much better than Θ̃(n^{1}/^{3}) which we show is the smallest possible with a single shuffler. We use our online summation algorithm to get algorithms with improved regret bounds for the contextual linear bandit problem. In particular we get optimal Õ(√n) regret with k = Ω̃(log n) concurrent shufflers.

Original language | English |
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Pages (from-to) | 33961-33982 |

Number of pages | 22 |

Journal | Proceedings of Machine Learning Research |

Volume | 202 |

State | Published - 2023 |

Event | 40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States Duration: 23 Jul 2023 → 29 Jul 2023 |

### Funding

Funders | Funder number |
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Yandex Initiative for Machine Learning | |

Horizon 2020 Framework Programme | 882396 |

Blavatnik Family Foundation | |

European Research Council | |

Israel Science Foundation | 993/17,1595/19,1871/19 |

Tel Aviv University |