论文标题
开放多代理系统中分散梯度下降的稳定性
Stability of Decentralized Gradient Descent in Open Multi-Agent Systems
论文作者
论文摘要
分散梯度下降（DGD）的目的是最大程度地减少互连代理持有的$ N $功能的总和。我们研究DGD在开放环境中的稳定性，代理可以加入或离开系统，每次增加或从全球目标中删除其功能。假设所有功能都是平稳的，强烈的凸出，并且它们的最小化都在给定的球中，我们表征了这些功能总和的全球最小化器的敏感性，以删除或添加新功能，并在$ o \ left中提供界限（\ min \ left（\ min \ left）（κ^^{0.5}，κ/n^0.5}，κ/n^0.5}，$ $ nirl， $κ$是条件号。我们还表明，所有代理人的状态最终都可以独立于到达和出发的顺序上。边界尺度的幅度具有互连的重要性，这也决定了在没有到达和出发的情况下最终解决方案的准确性，从而在准确性和灵敏度之间暴露了潜在的权衡。我们的分析依赖于DGD作为辅助功能的梯度下降的制定。使用Pesto工具箱分析我们的结果的紧密度。
The aim of decentralized gradient descent (DGD) is to minimize a sum of $n$ functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the addition or the removal of their function from the global objective. Assuming all functions are smooth, strongly convex, and their minimizers all lie in a given ball, we characterize the sensitivity of the global minimizer of the sum of these functions to the removal or addition of a new function and provide bounds in $ O\left(\min \left(κ^{0.5}, κ/n^{0.5},κ^{1.5}/n\right)\right)$ where $κ$ is the condition number. We also show that the states of all agents can be eventually bounded independently of the sequence of arrivals and departures. The magnitude of the bound scales with the importance of the interconnection, which also determines the accuracy of the final solution in the absence of arrival and departure, exposing thus a potential trade-off between accuracy and sensitivity. Our analysis relies on the formulation of DGD as gradient descent on an auxiliary function. The tightness of our results is analyzed using the PESTO Toolbox.
