Work

Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descent

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.03925

Authors: Lim, Debbie, Qiu, Yixian, Rebentrost, Patrick, Wang, Qisheng

Institutions: Computing Center, University of Edinburgh, Centre for Quantum Technologies, National University of Singapore

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation Singapore, QuantERA, Engineering and Physical Sciences Research Council

Awards: G5428356290, G8995634083

OpenAlex ID: W4404370627

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