Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descent

TL;DR

This paper introduces a quantum algorithm for sparse online learning that achieves quadratic speedup in high-dimensional data processing while maintaining theoretical regret bounds.

Contribution

It extends truncated gradient descent-based sparse online learning to the quantum setting, enabling faster processing of high-dimensional data.

Findings

Achieves quadratic speedup in time complexity with quantum access

Maintains a regret bound of O(1/√T) in online learning

Applicable to logistic regression, SVM, and least squares

Abstract

Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis makes the design of online learning algorithms that produce sparse solutions essential. The seminal work of \hyperlink{cite.langford2009sparse}{Langford, Li, and Zhang (2009)} developed a method to obtain sparsity via truncated gradient descent, showing a near-optimal online regret bound. Based on this method, we develop a quantum sparse online learning algorithm for logistic regression, the SVM, and least squares. Given efficient quantum access to the inputs, we show that a quadratic speedup in the time complexity with respect to the dimension of the problem is achievable, while maintaining a regret of $O(1/\sqrt{T})$, where $T$ is the number of iterations.