Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization
This work addresses non-convex optimization for distributed and shared-memory settings, offering incremental improvements in efficiency.
The authors tackled non-convex optimization by developing an asynchronous-parallel stochastic L-BFGS algorithm, achieving an ergodic convergence rate of O(1/√N) and showing significant speedup over synchronous distributed L-BFGS in experiments.
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.