arXiv:2602.00417stat.MLcs.LG2026-02

首次实现广义线性上下文强化学习的隐私保护,兼顾高效与安全。

Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits

  • 采用洗牌和联合差分隐私框架,解决无闭式解的优化难题。
  • 随机上下文下误差率仅比非隐私方案高√(d/ε)倍,对抗场景下近似最优。
  • 无需谱假设,适用于更广泛的真实场景,适合隐私敏感应用。

本文首次提出在洗牌差分隐私(shuffle DP)和联合差分隐私(joint DP)下的广义线性上下文赌博机算法。以往私有上下文赌博机研究局限于线性奖励模型(可闭式估计),而广义线性模型(GLMs)因无闭式解,需依赖私有凸优化;同时,隐私需跟踪多个动态设计矩阵,并将优化误差纳入后悔分析。针对两种隐私模型与上下文设置,我们分别设计算法:在随机上下文下,提出洗牌DP算法,后悔上界为$ ilde{O}(d^{3/2} oot rom{1}{2}T oot rom{1}{2} ext{log} T/ oot rom{1}{2} ext{ε})$,主导项相比非隐私情况仅多出$ oot rom{1}{2}d/ ext{ε}$因子;在对抗上下文下,提供联合DP算法,后悔为$ ilde{O}ig(d oot rom{1}{2}T ext{log} T + d^{3/4} oot rom{1}{2}T/ ext{ε} ext{ }( ext{log} T) ext{ }(d + ext{log} T)^{1/4}ig)$,主项与非隐私率$ ilde{O}(d oot rom{1}{2}T ext{log} T)$一致,隐私仅带来加性修正。与先前局部私有化GLM赌博机工作不同,本方法仅需上下文$ ext{ℓ}_2$有界,无需额外谱假设。

原文摘要 · Abstract (English)

We present the first algorithms for generalized linear contextual bandits under shuffle differential privacy and joint differential privacy. While prior work on private contextual bandits has been restricted to linear reward models -- which admit closed-form estimators -- generalized linear models (GLMs) pose fundamental new challenges: no closed-form estimator exists, requiring private convex optimization; privacy must be tracked across multiple evolving design matrices; and optimization error must be explicitly incorporated into regret analysis. We address these challenges under two privacy models and context settings. For stochastic contexts, we design a shuffle-DP algorithm achieving $\tilde{O}(d^{3/2}\sqrt{T \log T}/\sqrt{\varepsilon})$ regret in dominant term, differing from the non-private rate by a factor of $\sqrt{d/\varepsilon}$. For adversarial contexts, we provide a joint-DP algorithm with regret $\tilde{O}\!\big(d\sqrt{T} \log T + d^{3/4}\sqrt{T/\varepsilon}\,(\log T)\,(d + \log T)^{1/4}\big)$ -- matching the non-private rate $\tilde{O}(d\sqrt{T} \log T)$ in the leading term, with privacy contributing only an additive correction. Unlike prior work on locally private GLM bandits, our methods require no spectral assumptions on the context distribution beyond $\ell_2$ boundedness.

强化学习差分隐私上下文赌博机广义线性模型

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