相似性、压缩与局部步：分布式变分不等式高效通信的三大支柱
Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalities
AI总结：
本文首次将局部函数相似性、信息压缩和局部更新三种技术结合用于分布式变分不等式，提出具有最佳通信复杂度理论保证的新方法，并通过对抗学习实验验证其优越性。
摘要：
变分不等式是一类广泛而灵活的问题，包含最小化、鞍点和不动点问题作为特例。因此，变分不等式被用于从均衡搜索到对抗学习的各种应用。随着数据和模型规模的不断增大，当今的现实世界机器学习问题需要并行和分布式计算，其中大多数问题可以表示为变分不等式。与此同时，大多数分布式方法存在一个显著瓶颈——通信成本。减少总通信轮数以及单轮通信成本的三种主要技术是局部函数的相似性、传输信息的压缩和局部更新。在本文中，我们结合了所有这些方法。这种三重协同此前在变分不等式和鞍点问题中不存在，甚至在最小化问题中也不存在。本文提出的方法具有通信复杂度的最佳理论保证，并且显著领先于其他分布式变分不等式方法。理论结果通过在合成数据集和真实数据集上的对抗学习实验得到了验证。
英文摘要：
Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, and fixed point problems as special cases. Therefore, variational inequalities are used in various applications ranging from equilibrium search to adversarial learning. With the increasing size of data and models, today's instances demand parallel and distributed computing for real-world machine learning problems, most of which can be represented as variational inequalities. Meanwhile, most distributed approaches have a significant bottleneck - the cost of communications. The three main techniques to reduce the total number of communication rounds and the cost of one such round are the similarity of local functions, compression of transmitted information, and local updates. In this paper, we combine all these approaches. Such a triple synergy did not exist before for variational inequalities and saddle problems, nor even for minimization problems. The methods presented in this paper have the best theoretical guarantees of communication complexity and are significantly ahead of other methods for distributed variational inequalities. The theoretical results are confirmed by adversarial learning experiments on synthetic and real datasets.
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。
