Distributed Stochastic Gradient Tracking Algorithm With Variance Reduction for Non-Convex Optimization.

Area of Science:

• Distributed Optimization
• Machine Learning
• Signal Processing
• Non-convex Optimization

Background:

• Distributed optimization is crucial for large-scale problems in machine learning and signal processing.
• Existing methods struggle with variance in stochastic gradients within multiagent networks.
• Non-convex finite-sum optimization presents significant challenges in achieving global optima.

Purpose of the Study:

• To propose a novel distributed stochastic algorithm for general smooth non-convex finite-sum optimization.
• To address the variance introduced by local stochastic gradients in a distributed setting.
• To enhance convergence rates and reduce gradient complexity for multiagent network optimization.

Main Methods:

• Development of a modified variance reduction technique tailored for distributed stochastic gradients.
• Integration of gradient tracking and variance reduction to create the Gradient Tracking with Variance Reduction (GT-VR) algorithm.
• Rigorous theoretical analysis to prove convergence properties and complexity.

Main Results:

• The proposed GT-VR algorithm converges to first-order stationary points with a proven O(1/k) rate.
• GT-VR exhibits a lower gradient complexity of O(PMϵ^-1) compared to existing first-order methods.
• Numerical simulations confirm the superior efficiency of GT-VR against state-of-the-art algorithms.

Conclusions:

• The GT-VR algorithm offers an effective solution for large-scale non-convex finite-sum optimization in multiagent networks.
• The combination of gradient tracking and variance reduction significantly improves performance.
• The findings have practical implications for advancing distributed machine learning and signal processing applications.