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.

我们考虑高维度的随机情景线性赌博问题，在参数向量是 $s_{0}$- 稀疏的情况下，决策者受到差分隐私在中心模型和本地模型下的约束。我们提出了 PrivateLASSO，一种差分隐私的 LASSO 赌博算法，它基于两个子例程：(i) 基于稀疏硬阈值的隐私机制和 (ii) 用于识别参数 $	heta$ 支撑集的时序阈值规则。我们证明了最小化差分隐私的下界，并在标准假设下为 PrivateLASSO 在中心模型下建立了隐私和效用保证。