Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods
This work addresses optimization efficiency for machine learning practitioners, offering incremental improvements to existing variance-reducing methods.
The paper tackles the problem of improving variance reduction in stochastic optimization by using Hessian information to track gradients, achieving faster theoretical convergence rates near the optimum and demonstrating effectiveness across various problems.
Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.