Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization
Umut Simsekli, Cagatay Yildiz, Than Huy Nguyen, Taylan Cemgil, Gael Richard
Abstract
Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By building up on this recent theory, in this study, we develop an asynchronous-parallel stochastic L-BFGS algorithm for non-convex optimization. The proposed algorithm is suitable for both distributed and shared-memory settings. We provide formal theoretical analysis and show that the proposed method achieves an ergodic convergence rate of ${\cal O}(1/\sqrt{N})$ ($N$ being the total number of iterations) and it can achieve a linear speedup under certain conditions. We perform several experiments on both synthetic and real datasets. The results support our theory and show that the proposed algorithm provides a significant speedup over the recently proposed synchronous distributed L-BFGS algorithm.
BibTeX
@InProceedings{pmlr-v80-simsekli18a,
title = {Asynchronous Stochastic Quasi-{N}ewton {MCMC} for Non-Convex Optimization},
author = {Simsekli, Umut and Yildiz, Cagatay and Nguyen, Than Huy and Cemgil, Taylan and Richard, Gael},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {4674--4683},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/simsekli18a/simsekli18a.pdf},
url = {https://proceedings.mlr.press/v80/simsekli18a.html},
abstract = {Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By building up on this recent theory, in this study, we develop an asynchronous-parallel stochastic L-BFGS algorithm for non-convex optimization. The proposed algorithm is suitable for both distributed and shared-memory settings. We provide formal theoretical analysis and show that the proposed method achieves an ergodic convergence rate of ${\cal O}(1/\sqrt{N})$ ($N$ being the total number of iterations) and it can achieve a linear speedup under certain conditions. We perform several experiments on both synthetic and real datasets. The results support our theory and show that the proposed algorithm provides a significant speedup over the recently proposed synchronous distributed L-BFGS algorithm.}
}