Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints

10/25/2021

∙

by   Yanlin Chen, et al.

∙

6

∙

share

Lasso and Ridge are important minimization problems in machine learning and statistics. They are versions of linear regression with squared loss where the vector θ∈ℝ^d of coefficients is constrained in either ℓ_1-norm (for Lasso) or in ℓ_2-norm (for Ridge). We study the complexity of quantum algorithms for finding ε-minimizers for these minimization problems. We show that for Lasso we can get a quadratic quantum speedup in terms of d by speeding up the cost-per-iteration of the Frank-Wolfe algorithm, while for Ridge the best quantum algorithms are linear in d, as are the best classical algorithms.