提出SPDO方法，在去中心化优化中同时降低通信与计算开销。
Exploiting Similarity for Computation and Communication-Efficient Decentralized Optimization
- 通过稳定近端算子求解，降低子问题精度要求以减少计算量。
- 在函数相似性高的场景下，通信轮次和收敛速度均优于现有方法。
- 适合大规模分布式系统中的高效优化任务，尤其关注通信效率的场景。
降低通信复杂度对高效去中心化优化至关重要。近端去中心化优化（PDO）框架因其能利用节点间局部函数的相似性来减少通信轮次而备受关注。当不同节点的局部函数相似时，该类方法可在更少通信步数内实现更快收敛。然而，现有PDO方法通常需要高精度求解与近端算子相关的子问题，导致显著计算开销。本文提出稳定近端去中心化优化（SPDO）方法，在PDO框架内实现了当前最优的通信与计算复杂度。此外，我们通过放宽子问题精度要求并利用平均函数相似性，改进了现有方法的理论分析。实验结果表明，SPDO显著优于现有方法。
原文摘要 · Abstract (English)
Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity among nodes to reduce communication rounds. Specifically, when local functions at different nodes are similar, these methods achieve faster convergence with fewer communication steps. However, existing PDO methods often require highly accurate solutions to subproblems associated with the proximal operator, resulting in significant computational overhead. In this work, we propose the Stabilized Proximal Decentralized Optimization (SPDO) method, which achieves state-of-the-art communication and computational complexities within the PDO framework. Additionally, we refine the analysis of existing PDO methods by relaxing subproblem accuracy requirements and leveraging average functional similarity. Experimental results demonstrate that SPDO significantly outperforms existing methods.
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