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arXiv 2409.19092cs.LGcs.CRstat.ML
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具有差分隐私的联邦在线专家预测:分离性与遗憾加速

Federated Online Prediction from Experts with Differential Privacy: Separations and Regret Speed-ups

School of EECS, The Pennsylvania State University(宾夕法尼亚州立大学电机工程与计算机科学学院)

Fengyu Gao, Ruiquan Huang, Jing Yang

AI总结:

本文首次研究联邦场景下具有差分隐私的在线专家预测问题,提出 Fed-DP-OPE-Stoch 和 Fed-SVT 两种算法,分别在随机对手和低损失遗忘对手情形下实现遗憾加速,并证明遗忘对手一般情形下协作无法带来加速。

摘要:

我们研究在随机对手和遗忘对手两种情形下,具有差分隐私的联邦在线专家预测问题。我们的目标是在时间范围 $T$ 内,使 $m$ 个并行工作的客户端在显式差分隐私(DP)保证下最小化平均遗憾。针对随机对手,我们提出 Fed-DP-OPE-Stoch 算法,在纯 DP 和近似 DP 约束下,与单玩家对应方法相比,该算法实现了每客户端遗憾的 $\sqrt{m}$ 倍加速,同时保持对数级别的通信成本。针对遗忘对手,我们建立了非平凡的下界,表明在一般遗忘对手情形下,客户端之间的协作不会带来遗憾加速。随后我们考虑遗忘对手设置的一个特例,即存在一个低损失专家。我们设计了一种新算法 Fed-SVT,并证明在纯 DP 和近似 DP 约束下,与单玩家对应方法相比,它实现了 $m$ 倍的遗憾加速。我们的下界表明 Fed-SVT 在对数因子范围内接近最优。实验证明了我们所提算法的有效性。据我们所知,这是首个在联邦设置下研究具有差分隐私的在线专家预测的工作。

英文摘要:

We study the problems of differentially private federated online prediction from experts against both stochastic adversaries and oblivious adversaries. We aim to minimize the average regret on $m$ clients working in parallel over time horizon $T$ with explicit differential privacy (DP) guarantees. With stochastic adversaries, we propose a Fed-DP-OPE-Stoch algorithm that achieves $\sqrt{m}$-fold speed-up of the per-client regret compared to the single-player counterparts under both pure DP and approximate DP constraints, while maintaining logarithmic communication costs. With oblivious adversaries, we establish non-trivial lower bounds indicating that collaboration among clients does not lead to regret speed-up with general oblivious adversaries. We then consider a special case of the oblivious adversaries setting, where there exists a low-loss expert. We design a new algorithm Fed-SVT and show that it achieves an $m$-fold regret speed-up under both pure DP and approximate DP constraints over the single-player counterparts. Our lower bound indicates that Fed-SVT is nearly optimal up to logarithmic factors. Experiments demonstrate the effectiveness of our proposed algorithms. To the best of our knowledge, this is the first work examining the differentially private online prediction from experts in the federated setting.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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