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- W2411556044 abstract "The cyclic block coordinate descent-type (CBCD-type) methods have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical machine learning methods such as elastic-net regression, ridge penalized logistic regression, and sparse additive regression. Existing optimization literature has shown that the CBCD-type methods attain iteration complexity of $O(pcdotlog(1/epsilon))$, where $epsilon$ is a pre-specified accuracy of the objective value, and $p$ is the number of blocks. However, such iteration complexity explicitly depends on $p$, and therefore is at least $p$ times worse than those of gradient descent methods. To bridge this theoretical gap, we propose an improved convergence analysis for the CBCD-type methods. In particular, we first show that for a family of quadratic minimization problems, the iteration complexity of the CBCD-type methods matches that of the gradient descent methods in term of dependency on $p$ (up to a $log^2 p$ factor). Thus our complexity bounds are sharper than the existing bounds by at least a factor of $p/log^2p$. We also provide a lower bound to confirm that our improved complexity bounds are tight (up to a $log^2 p$ factor) if the largest and smallest eigenvalues of the Hessian matrix do not scale with $p$. Finally, we generalize our analysis to other strongly convex minimization problems beyond quadratic ones" @default.
- W2411556044 created "2016-06-24" @default.
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- W2411556044 date "2016-07-10" @default.
- W2411556044 modified "2023-09-28" @default.
- W2411556044 title "An Improved Convergence Analysis of Cyclic Block Coordinate Descent-type Methods for Strongly Convex Minimization" @default.
- W2411556044 hasPublicationYear "2016" @default.
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