论文标题
通过网络大小独立问题进行分散优化的自动化绩效估计
Automated Performance Estimation for Decentralized Optimization via Network Size Independent Problems
论文作者
论文摘要
我们为分散优化的性能估计问题（PEP）开发了一种新颖的表述，该优化的大小独立于网络中的代理数量。 PEP方法允许通过求解SDP来自动计算最差的案例性能和一阶优化方法的最坏情况。与以前的工作不同，我们新的PEP公式的大小独立于网络尺寸。为此，我们对分散的问题进行全球视图，还可以使共识子空间及其正交补充分离。我们将我们的方法应用于不同的分散方法，例如DGD，DIGing和Extra，并获得对任何网络大小有效的数值紧密性能保证。
We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case performance and worst-case instance of first-order optimization methods by solving an SDP. Unlike previous work, the size of our new PEP formulation is independent of the network size. For this purpose, we take a global view of the decentralized problem and we also decouple the consensus subspace and its orthogonal complement. We apply our methodology to different decentralized methods such as DGD, DIGing and EXTRA and obtain numerically tight performance guarantees that are valid for any network size.
