Papers › Online Second Order Methods for Non-Convex Stochastic Optimizations
Online Second Order Methods for Non-Convex Stochastic Optimizations
Xi-Lin Li
This paper proposes a family of online second order methods for possibly non-convex stochastic optimizations based on the theory of preconditioned stochastic gradient descent (PSGD), which can be regarded as an enhance stochastic Newton method with the ability to handle gradient noise and non-convexity simultaneously. We have improved the implementations of the original PSGD in several ways, e.g., new forms of preconditioners, more accurate Hessian vector product calculations, and better numerical stability with vanishing or ill-conditioned Hessian, etc.. We also have unrevealed the relationship between feature normalization and PSGD with Kronecker product preconditioners, which explains the excellent performance of Kronecker product preconditioners in deep neural network learning. A software package (https://github.com/lixilinx/psgd_tf) implemented in Tensorflow is provided to compare variations of stochastic gradient descent (SGD) and PSGD with five different preconditioners on a wide range of benchmark problems with commonly used neural network architectures, e.g., convolutional and recurrent neural networks. Experimental results clearly demonstrate the advantages of PSGD in terms of generalization performance and convergence speed.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
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.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
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