We consider a high-dimensional stochastic contextual linear bandit problem when the parameter vector is $s_{0}$-sparse and the decision maker is subject to privacy constraints under both central and local models of differential privacy. We present PrivateLASSO, a differentially private LASSO bandit algorithm. PrivateLASSO is based on two sub-routines: (i) a sparse hard-thresholding-based privacy mechanism and (ii) an episodic thresholding rule for identifying the support of the parameter $\theta$. We prove minimax private lower bounds and establish privacy and utility guarantees for PrivateLASSO for the central model under standard assumptions.

翻译：我们考虑当参数向量是$s_{0}$-稀疏的，且决策者在差分隐私的中央模型和局部模型下受到隐私约束时的高维随机情境线性赌博机问题。我们提出了PrivateLASSO，一种差分隐私LASSO赌博机算法。PrivateLASSO基于两个子程序：(i) 一种基于稀疏硬阈值的隐私机制和(ii) 一种用于识别参数$\theta$支撑集的阶段式阈值规则。我们证明了极小化极大的隐私下界，并在标准假设下为中央模型下的PrivateLASSO建立了隐私和效用保证。