Optimal Asynchronous Stochastic Nonconvex Optimization under Heavy-Tailed Noise

2026-01-27

AI Summary

This work addresses the challenges posed by heavy-tailed gradient noise and highly heterogeneous computation times across workers in asynchronous stochastic nonconvex optimization. The authors propose a momentum-based asynchronous normalized stochastic gradient descent algorithm that, under the mild assumption of bounded $p$-th central moments of the gradient noise for $p \in (1,2]$, achieves optimal time complexity in arbitrarily heterogeneous computing environments. Theoretical analysis establishes both convergence and optimality of the proposed method, while numerical experiments further demonstrate its robustness and effectiveness in settings with heavy-tailed noise distributions.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across workers. We propose an asynchronous normalized stochastic gradient descent algorithm with momentum. The analysis show that our method achieves the optimal time complexity under the assumption of bounded $p$th-order central moment with $p\in(1,2]$. We also provide numerical experiments to show the effectiveness of proposed method.

Problem

• asynchronous optimization
• stochastic nonconvex optimization
• heavy-tailed noise
• heterogeneous computation times

Innovation

• asynchronous optimization
• heavy-tailed noise
• normalized SGD
• nonconvex optimization
• optimal time complexity