Papers › Parallel Coordinate Descent Newton Method for Efficient ℓ₁-Regularized Minimization
Parallel Coordinate Descent Newton Method for Efficient ℓ₁-Regularized Minimization
An Bian, Xiong Li, Yuncai Liu, Ming-Hsuan Yang
The recent years have witnessed advances in parallel algorithms for large scale optimization problems. Notwithstanding demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under high parallelism or require data preprocessing to alleviate these problems. In this work, we propose a Parallel Coordinate Descent Newton algorithm using multidimensional approximate Newton steps (PCDN), where the off-diagonal elements of the Hessian are set to zero to enable parallelization. It randomly partitions the feature set into b bundles/subsets with size of P, and sequentially processes each bundle by first computing the descent directions for each feature in parallel and then conducting P-dimensional line search to obtain the step size. We show that: (1) PCDN is guaranteed to converge globally despite increasing parallelism; (2) PCDN converges to the specified accuracy ϵ within the limited iteration number of T_ϵ, and T_ϵ decreases with increasing parallelism (bundle size P). Using the implementation technique of maintaining intermediate quantities, we minimize the data transfer and synchronization cost of the P-dimensional line search. For concreteness, the proposed PCDN algorithm is applied to ℓ₁-regularized logistic regression and ℓ₂-loss SVM. Experimental evaluations on six benchmark datasets show that the proposed PCDN algorithm exploits parallelism well and outperforms the state-of-the-art methods in speed without losing accuracy.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections