arXiv:2410.20250stat.MLcs.LG2024-10ICML

在联邦学习中,用源网络数据给未知目标网络的模型性能提供可证明的保障。

Certifiably Robust Model Evaluation in Federated Learning under Meta-Distributional Shifts

  • 基于源网络数据,推导出目标网络上模型损失和风险分布的最坏情况保证
  • 提出新型鲁棒DKW不等式,支持对未知分布下模型表现的可验证评估
  • 适用于隐私敏感场景,且在客户端数量多时效果更优

我们解决在仅使用训练模型的源网络测量值的情况下,对未见目标网络上联邦学习模型性能进行可证明保障的挑战。考虑一个包含K个客户端的源网络A,每个客户端持有来自异质分布的私有非独立同分布数据,这些分布可建模为更广泛元分布μ的样本。目标是在未知元分布μ'的另一未见网络B上,对模型性能提供可证明的保证,假设μ与μ'之间的偏差在Wasserstein距离或f-散度下有界。我们推导出模型平均损失和其风险累积分布函数(CDF)的最坏情况统一保证,后者对应一种新型对抗鲁棒的Dvoretzky-Kiefer-Wolfowitz(DKW)不等式。此外,我们展示原始DKW界如何实现对同一源网络内未见客户端真实性能的合理认证。我们的边界高效可计算,渐近最小最大最优,并保持客户端隐私。我们还建立了非渐近泛化边界,当客户端数量K增大且每个客户端最小样本量超过𝒪(log K)时,该边界收敛至零。实证评估证实了所提边界的实际效用,涵盖多个真实任务。项目代码已公开于:github.com/samin-mehdizadeh/Robust-Evaluation-DKW

原文摘要 · Abstract (English)

We address the challenge of certifying the performance of a federated learning model on an unseen target network using only measurements from the source network that trained the model. Specifically, consider a source network "A" with $K$ clients, each holding private, non-IID datasets drawn from heterogeneous distributions, modeled as samples from a broader meta-distribution $μ$. Our goal is to provide certified guarantees for the model's performance on a different, unseen network "B", governed by an unknown meta-distribution $μ'$, assuming the deviation between $μ$ and $μ'$ is bounded either in Wasserstein distance or an $f$-divergence. We derive worst-case uniform guarantees for both the model's average loss and its risk CDF, the latter corresponding to a novel, adversarially robust version of the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality. In addition, we show how the vanilla DKW bound enables principled certification of the model's true performance on unseen clients within the same (source) network. Our bounds are efficiently computable, asymptotically minimax optimal, and preserve clients' privacy. We also establish non-asymptotic generalization bounds that converge to zero as $K$ grows and the minimum per-client sample size exceeds $\mathcal{O}(\log K)$. Empirical evaluations confirm the practical utility of our bounds across real-world tasks. The project code is available at: github.com/samin-mehdizadeh/Robust-Evaluation-DKW

联邦学习鲁棒评估分布偏移可证明保障

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