Differentially Private High Dimensional Bandits

• URL: http://arxiv.org/abs/2402.03737v1
• Date: Tue, 6 Feb 2024 06:10:46 GMT
• Title: Differentially Private High Dimensional Bandits
• Authors: Apurv Shukla
• Abstract summary: 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 $theta$.
• Score: 1.3597551064547502
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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