Stochastic Gradient Variance Reduction by Solving a Filtering Problem

TL;DR

This paper introduces Filter Gradient Descent (FGD), a novel stochastic optimization method that reduces gradient variance by solving an adaptive filtering problem, leading to more reliable gradient estimates and faster neural network training.

Contribution

The paper presents the first practical integration of filtering techniques into gradient estimation for stochastic optimization, improving convergence and robustness.

Findings

FGD outperforms traditional methods in neural network training.

The method effectively reduces gradient variance in numerical optimization.

FGD accelerates convergence compared to momentum-based algorithms.

Abstract

Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad convergence. In this paper, we propose \textbf{Filter Gradient Decent}~(FGD), an efficient stochastic optimization algorithm that makes the consistent estimation of the local gradient by solving an adaptive filtering problem with different design of filters. Our method reduces variance in stochastic gradient descent by incorporating the historical states to enhance the current estimation. It is able to correct noisy gradient direction as well as to accelerate the convergence of learning. We demonstrate the effectiveness of the proposed Filter Gradient Descent on numerical optimization and training neural networks, where it achieves superior and robust performance compared with traditional momentum-based methods. To the best of our knowledge, we are the first to provide a practical solution that integrates filtering into gradient estimation by making the analogy between gradient estimation and filtering problems in signal processing. (The code is provided in https://github.com/Adamdad/Filter-Gradient-Decent)