4 research outputs found
Quantum differentially private sparse regression learning
Differentially private (DP) learning, which aims to accurately extract
patterns from the given dataset without exposing individual information, is an
important subfield in machine learning and has been extensively explored.
However, quantum algorithms that could preserve privacy, while outperform their
classical counterparts, are still lacking. The difficulty arises from the
distinct priorities in DP and quantum machine learning, i.e., the former
concerns a low utility bound while the latter pursues a low runtime cost. These
varied goals request that the proposed quantum DP algorithm should achieve the
runtime speedup over the best known classical results while preserving the
optimal utility bound.
The Lasso estimator is broadly employed to tackle the high dimensional sparse
linear regression tasks. The main contribution of this paper is devising a
quantum DP Lasso estimator to earn the runtime speedup with the privacy
preservation, i.e., the runtime complexity is with
a nearly optimal utility bound , where is the sample
size and is the data dimension with . Since the optimal classical
(private) Lasso takes runtime, our proposal achieves quantum
speedups when . There are two key components in our algorithm.
First, we extend the Frank-Wolfe algorithm from the classical Lasso to the
quantum scenario, {where the proposed quantum non-private Lasso achieves a
quadratic runtime speedup over the optimal classical Lasso.} Second, we develop
an adaptive privacy mechanism to ensure the privacy guarantee of the
non-private Lasso. Our proposal opens an avenue to design various learning
tasks with both the proven runtime speedups and the privacy preservation