Related papers: On the Growth of Mistakes in Differentially Private Online Learning: A Lower Bound Perspective

On the Growth of Mistakes in Differentially Private Online Learning: A Lower Bound Perspective

URL: http://arxiv.org/abs/2402.16778v1
Date: Mon, 26 Feb 2024 17:49:37 GMT
Title: On the Growth of Mistakes in Differentially Private Online Learning: A Lower Bound Perspective
Authors: Daniil Dmitriev, Krist\'of Szab\'o, Amartya Sanyal
Abstract summary: We provide lower bounds for Differentially Private (DP) Online Learning algorithms. Our work is the first result towards settling lower bounds for DP-Online learning.
Score: 9.108253909440489
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this paper, we provide lower bounds for Differentially Private (DP) Online Learning algorithms. Our result shows that, for a broad class of $(\varepsilon,\delta)$-DP online algorithms, for $T$ such that $\log T\leq O(1 / \delta)$, the expected number of mistakes incurred by the algorithm grows as $\Omega(\log \frac{T}{\delta})$. This matches the upper bound obtained by Golowich and Livni (2021) and is in contrast to non-private online learning where the number of mistakes is independent of $T$. To the best of our knowledge, our work is the first result towards settling lower bounds for DP-Online learning and partially addresses the open question in Sanyal and Ramponi (2022).

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