Differentially Private High Dimensional Bandits
This work addresses privacy-preserving decision-making in bandit settings, which is incremental as it adapts existing methods to privacy constraints.
The paper tackles the problem of high-dimensional stochastic contextual linear bandits with sparse parameters under differential privacy constraints, presenting PrivateLASSO, an algorithm that achieves privacy and utility guarantees with minimax lower bounds.
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 $θ$. We prove minimax private lower bounds and establish privacy and utility guarantees for PrivateLASSO for the central model under standard assumptions.