具有非协调步长的几何收敛分布式优化
Geometrically Convergent Distributed Optimization with Uncoordinated Step-Sizes
AI总结：
本文研究了在非协调步长下，ATC变体的DIGing算法的收敛速率，证明其在不同步长下仍能几何快速收敛，并表明ATC结构比原始DIGing算法中的DGD结构更高效。
摘要：
最近一种分布式优化算法家族，DIGing的，已被证明在时间变化的无向/有向图上具有几何收敛性。然而，需要所有代理使用相同的步长。在本文中，我们研究了在非协调步长下，ATC变体的DIGing算法的收敛速率。我们证明即使代理间的步长不同，ATC变体的DIGing算法仍能几何快速收敛。此外，我们的分析表明，与原始DIGing算法中使用的分布式梯度下降（DGD）结构相比，ATC结构可以加速收敛。
英文摘要：
A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC variation of DIGing algorithm converges geometrically fast even if the step-sizes are different among the agents. In addition, our analysis implies that the ATC structure can accelerate convergence compared to the distributed gradient descent (DGD) structure which has been used in the original DIGing algorithm.
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