Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization

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Umut Simsekli, Cagatay Yildiz, Than Huy Nguyen, Taylan Cemgil, Gael Richard ;
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4674-4683, 2018.

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.

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