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arXiv · 2411.03925

Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descent

Debbie Lim·Yixian Qiu·Patrick Rebentrost·Qisheng Wang
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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.

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Debbie Lim, Yixian Qiu, Patrick Rebentrost, Qisheng Wang. 2024-11-06. Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descent. https://arxiv.org/abs/2411.03925

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