论文标题
非凸出分布式优化的双重平均速率分析
Rate analysis of dual averaging for nonconvex distributed optimization
论文作者
论文摘要
这项工作研究了非凸出的分布式在随机通信网络上的约束优化。我们重新访问分布式双重平均算法，该算法已知会因凸问题而收敛。我们从集中式案例开始，该案例将两个连续更新的更改视为次优度度量。我们通过证明其与平稳性密切相关来验证使用这种度量的使用。这为我们提供了研究非凸优化中双重平均的收敛性的手柄。我们证明，此次优小度度量的平方规范以$ \ MATHCAL {O}（1/T）$收敛。然后，对于分布式设置，我们以$ \ MATHCAL {O}（1/T）$的价格显示融合到固定点。最后，给出了一个数字示例来说明我们的理论结果。
This work studies nonconvex distributed constrained optimization over stochastic communication networks. We revisit the distributed dual averaging algorithm, which is known to converge for convex problems. We start from the centralized case, for which the change of two consecutive updates is taken as the suboptimality measure. We validate the use of such a measure by showing that it is closely related to stationarity. This equips us with a handle to study the convergence of dual averaging in nonconvex optimization. We prove that the squared norm of this suboptimality measure converges at rate $\mathcal{O}(1/t)$. Then, for the distributed setup we show convergence to the stationary point at rate $\mathcal{O}(1/t)$. Finally, a numerical example is given to illustrate our theoretical results.
