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arXiv 2406.20006cs.LG
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分布式学习中平坦性与优化之间的权衡

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

Institute of Electrical and Micro Engineering in EPFL(瑞士联邦理工学院电气与微电子工程学院);Sun Yat-sen University(中山大学);Center for Machine Learning Research (CMLR) in Peking University(北京大学机器学习研究中心)

Ying Cao, Zhaoxian Wu, Kun Yuan, Ali H. Sayed

AI总结:

本文通过理论框架分析分布式学习中平坦性与优化性能的权衡,发现去中心化策略尤其是扩散方法能更快逃离局部极小值并取得更优的平坦性-优化平衡,从而提升分类准确率。

摘要:

本文提出了一个理论框架,用于评估和比较分布式学习中随机梯度算法的性能,重点关注它们在非凸环境中局部极小值附近的行为。此前的研究已经注意到,向平坦局部极小值收敛往往能增强学习算法的泛化能力。本文发现了三个有趣的结果。第一,研究表明,与集中式方案相比,去中心化学习策略能够更快地逃离局部极小值,并更倾向于收敛到更平坦的极小值。第二,在去中心化方法中,共识策略的 excess-risk 性能比扩散策略更差,这使其有更大的机会逃离局部极小值并倾向于更平坦的极小值。第三,也是重要的一点,最终的分类准确率不仅仅取决于局部极小值的平坦性,还取决于学习算法能够多好地逼近该极小值。换句话说,分类准确率是平坦性和优化性能两者的函数。在这方面,由于扩散策略的 excess-risk 低于共识策略,当两种算法都从随机初始点开始训练时,扩散策略能够提高分类准确率。本文深入考察了平坦性和优化误差这两个度量之间的相互作用。一个重要的结论是,去中心化策略通常能够提供更高的分类准确率,因为与集中式方案相比,它们在平坦性和优化性能之间取得了更有利的平衡。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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