On the Trade-off between Flatness and Optimization in Distributed Learning

2024-06-28

IEEE Transactions on Pattern Analysis and Machine Intelligence

AI Summary

This work investigates the synergistic interplay between model flatness and optimization accuracy in governing generalization performance within distributed nonconvex learning. We propose a unified theoretical framework integrating nonconvex optimization, decentralized signal processing, and excess risk analysis, and rigorously establish— for the first time—that diffusion-type decentralized algorithms outperform both centralized and consensus-based counterparts in jointly balancing flatness and optimization error. Our theory demonstrates that classification accuracy is jointly determined by flatness and optimization precision, not flatness alone, and that diffusion strategies substantially reduce excess risk. Extensive experiments on standard benchmarks corroborate the superior generalization of diffusion-based methods. The core contribution lies in characterizing the fundamental flatness–accuracy trade-off and establishing diffusion dynamics as a principled paradigm for enhancing generalization in distributed learning.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Distributed Machine Learning & Federated Learning
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have noticed that convergence toward flat local minima tend to enhance the generalization ability of learning algorithms. This work discovers three interesting results. First, it shows that decentralized learning strategies are able to escape faster away from local minima and favor convergence toward flatter minima relative to the centralized solution. Second, in decentralized methods, the consensus strategy has a worse excess-risk performance than diffusion, giving it a better chance of escaping from local minima and favoring flatter minima. Third, and importantly, the ultimate classification accuracy is not solely dependent on the flatness of the local minimum but also on how well a learning algorithm can approach that minimum. In other words, the classification accuracy is a function of both flatness and optimization performance. In this regard, since diffusion has a lower excess-risk than consensus, when both algorithms are trained starting from random initial points, diffusion enhances the classification accuracy. The paper examines the interplay between the two measures of flatness and optimization error closely. One important conclusion is that decentralized strategies deliver in general enhanced classification accuracy because they strike a more favorable balance between flatness and optimization performance compared to the centralized solution.

Problem

• Evaluates decentralized vs centralized learning in nonconvex optimization
• Compares flatness and optimization impact on classification accuracy
• Analyzes diffusion and consensus strategies for escaping local minima

Innovation

• Decentralized learning escapes local minima faster
• Diffusion outperforms consensus in excess-risk
• Accuracy depends on flatness and optimization balance