PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent

Cho-Jui Hsieh, Hsiang-Fu Yu, Inderjit Dhillon
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:2370-2379, 2015.

Abstract

Stochastic Dual Coordinate Descent (DCD) is one of the most efficient ways to solve the family of L2-regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla implementation of DCD is quite slow; however, by maintaining primal variables while updating dual variables, the time complexity of DCD can be significantly reduced. Such a strategy forms the core algorithm in the widely-used LIBLINEAR package. In this paper, we parallelize the DCD algorithms in LIBLINEAR. In recent research, several synchronized parallel DCD algorithms have been proposed, however, they fail to achieve good speedup in the shared memory multi-core setting. In this paper, we propose a family of parallel asynchronous stochastic dual coordinate descent algorithms (PASSCoDe). Each thread repeatedly selects a random dual variable and conducts coordinate updates using the primal variables that are stored in the shared memory. We analyze the convergence properties of DCD when different locking/atomic mechanisms are applied. For implementation with atomic operations, we show linear convergence under mild conditions. For implementation without any atomic operations or locking, we present a novel error analysis for PASSCoDe under the multi-core environment, showing that the converged solution is the exact solution for a primal problem with a perturbed regularizer. Experimental results show that our methods are much faster than previous parallel coordinate descent solvers.

Cite this Paper


BibTeX
@InProceedings{pmlr-v37-hsieha15, title = {PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent}, author = {Hsieh, Cho-Jui and Yu, Hsiang-Fu and Dhillon, Inderjit}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {2370--2379}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/hsieha15.pdf}, url = { http://proceedings.mlr.press/v37/hsieha15.html }, abstract = {Stochastic Dual Coordinate Descent (DCD) is one of the most efficient ways to solve the family of L2-regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla implementation of DCD is quite slow; however, by maintaining primal variables while updating dual variables, the time complexity of DCD can be significantly reduced. Such a strategy forms the core algorithm in the widely-used LIBLINEAR package. In this paper, we parallelize the DCD algorithms in LIBLINEAR. In recent research, several synchronized parallel DCD algorithms have been proposed, however, they fail to achieve good speedup in the shared memory multi-core setting. In this paper, we propose a family of parallel asynchronous stochastic dual coordinate descent algorithms (PASSCoDe). Each thread repeatedly selects a random dual variable and conducts coordinate updates using the primal variables that are stored in the shared memory. We analyze the convergence properties of DCD when different locking/atomic mechanisms are applied. For implementation with atomic operations, we show linear convergence under mild conditions. For implementation without any atomic operations or locking, we present a novel error analysis for PASSCoDe under the multi-core environment, showing that the converged solution is the exact solution for a primal problem with a perturbed regularizer. Experimental results show that our methods are much faster than previous parallel coordinate descent solvers.} }
Endnote
%0 Conference Paper %T PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent %A Cho-Jui Hsieh %A Hsiang-Fu Yu %A Inderjit Dhillon %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-hsieha15 %I PMLR %P 2370--2379 %U http://proceedings.mlr.press/v37/hsieha15.html %V 37 %X Stochastic Dual Coordinate Descent (DCD) is one of the most efficient ways to solve the family of L2-regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla implementation of DCD is quite slow; however, by maintaining primal variables while updating dual variables, the time complexity of DCD can be significantly reduced. Such a strategy forms the core algorithm in the widely-used LIBLINEAR package. In this paper, we parallelize the DCD algorithms in LIBLINEAR. In recent research, several synchronized parallel DCD algorithms have been proposed, however, they fail to achieve good speedup in the shared memory multi-core setting. In this paper, we propose a family of parallel asynchronous stochastic dual coordinate descent algorithms (PASSCoDe). Each thread repeatedly selects a random dual variable and conducts coordinate updates using the primal variables that are stored in the shared memory. We analyze the convergence properties of DCD when different locking/atomic mechanisms are applied. For implementation with atomic operations, we show linear convergence under mild conditions. For implementation without any atomic operations or locking, we present a novel error analysis for PASSCoDe under the multi-core environment, showing that the converged solution is the exact solution for a primal problem with a perturbed regularizer. Experimental results show that our methods are much faster than previous parallel coordinate descent solvers.
RIS
TY - CPAPER TI - PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent AU - Cho-Jui Hsieh AU - Hsiang-Fu Yu AU - Inderjit Dhillon BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-hsieha15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 2370 EP - 2379 L1 - http://proceedings.mlr.press/v37/hsieha15.pdf UR - http://proceedings.mlr.press/v37/hsieha15.html AB - Stochastic Dual Coordinate Descent (DCD) is one of the most efficient ways to solve the family of L2-regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla implementation of DCD is quite slow; however, by maintaining primal variables while updating dual variables, the time complexity of DCD can be significantly reduced. Such a strategy forms the core algorithm in the widely-used LIBLINEAR package. In this paper, we parallelize the DCD algorithms in LIBLINEAR. In recent research, several synchronized parallel DCD algorithms have been proposed, however, they fail to achieve good speedup in the shared memory multi-core setting. In this paper, we propose a family of parallel asynchronous stochastic dual coordinate descent algorithms (PASSCoDe). Each thread repeatedly selects a random dual variable and conducts coordinate updates using the primal variables that are stored in the shared memory. We analyze the convergence properties of DCD when different locking/atomic mechanisms are applied. For implementation with atomic operations, we show linear convergence under mild conditions. For implementation without any atomic operations or locking, we present a novel error analysis for PASSCoDe under the multi-core environment, showing that the converged solution is the exact solution for a primal problem with a perturbed regularizer. Experimental results show that our methods are much faster than previous parallel coordinate descent solvers. ER -
APA
Hsieh, C., Yu, H. & Dhillon, I.. (2015). PASSCoDe: Parallel ASynchronous Stochastic dual Co-ordinate Descent. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:2370-2379 Available from http://proceedings.mlr.press/v37/hsieha15.html .

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