Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descent
Keywords: Quantum algorithms, online learning, truncated gradient descent, logistic regression, support vector machine, least squares
TL;DR: This paper proposes a quantum sparse online learning algorithm via truncated gradient descent, achieving a quadratic speedup in the data dimension for logistic regression, SVMs, and least squares in the online setting.
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 Langford \emph{et al.} 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 time steps.
Primary Area: learning theory
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Submission Number: 10500
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