2013/11/08 by Jascha Sohl-Dickstein, Jascha Sohl‐Dickstein, Sohl-Dickstein, Jascha +4 · 1 voice · 3 citations
Computer Science · Engineering · #90C26 #Advanced Image Processing Techniques #FOS: Computer and information sciences #G.1.6 #Machine Learning (cs.LG) #Neural Networks and Applications #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #cs.LG
paper · pdf · doi:10.48550/arxiv.1311.2115
openalex publication_date 2013/11/08 · arxiv published 2013/11/09 · arxiv updated 2014/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these disparate approaches by maintaining an independent Hessian approximation for each contributing function in the sum. We maintain computational tractability and limit memory requirements even for high dimensional optimization problems by storing and manipulating these quadratic approximations in a shared, time evolving, low dimensional subspace. Each update step requires only a single contributing function or minibatch evaluation (as in SGD), and each step is scaled using an approximate inverse Hessian and little to no adjustment of hyperparameters is required (as is typical for quasi-Newton methods). This algorithm contrasts with earlier stochastic second order techniques that treat the Hessian of each contributing function as a noisy approximation to the full Hessian, rather than as a target for direct estimation. We experimentally demonstrate improved convergence on seven diverse optimization problems. The algorithm is released as open source Python and MATLAB packages.