# Differentially Private High Dimensional Bandits

arXiv: https://arxiv.org/abs/2402.03737 · HTML: https://mlsanity.com/paper/2402.03737/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Locally Differentially Private (Contextual) Bandits Learning](https://mlsanity.com/paper/2006.00701/) (2020)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Adaptive Exploration in Linear Contextual Bandit](https://mlsanity.com/paper/1910.06996/) (2019)
- [Multi-Armed Bandits with Local Differential Privacy](https://mlsanity.com/paper/2007.03121/) (2020)
- [Local, Private, Efficient Protocols for Succinct Histograms](https://mlsanity.com/paper/1504.04686/) (2015)
- [Generalized Linear Bandits with Local Differential Privacy](https://mlsanity.com/paper/2106.03365/) (2021)
- [Private Matchings and Allocations](https://mlsanity.com/paper/1311.2828/) (2013)
- [Privacy-Preserving Dynamic Personalized Pricing with Demand Learning](https://mlsanity.com/paper/2009.12920/) (2020)
- [A Simple Unified Framework for High Dimensional Bandit Problems](https://mlsanity.com/paper/2102.09626/) (2021)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [Thresholded Lasso Bandit](https://mlsanity.com/paper/2010.11994/) (2020)
- [The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds](https://mlsanity.com/paper/2011.03900/) (2020)
- [Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression](https://mlsanity.com/paper/1507.00056/) (2015)
- [Asymptotically Truthful Equilibrium Selection in Large Congestion Games](https://mlsanity.com/paper/1311.2625/) (2013)
- [PAPRIKA: Private Online False Discovery Rate Control](https://mlsanity.com/paper/2002.12321/) (2020)
- [The Possibilities and Limitations of Private Prediction Markets](https://mlsanity.com/paper/1602.07362/) (2016)

## Abstract (arXiv)

We consider a high-dimensional stochastic contextual linear bandit problem when the parameter vector is s0-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.