开放多智能体系统中用于资源分配的随机坐标下降法
Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems
AI总结：
本文针对开放多智能体系统中的可分离资源分配问题，提出基于随机坐标下降的时变优化分析方法，建立封闭系统线性收敛性和开放系统稳定性条件，刻画收敛速度与智能体替换鲁棒性之间的权衡。
摘要：
我们提出一种方法，用于分析分布式随机坐标下降算法在开放多智能体系统背景下求解可分离资源分配问题的性能，其中智能体在过程中可以被替换。特别地，我们通过采用一种时变优化方法来刻画到极小点的距离在期望意义下的演化，该方法建立在两个组成部分之上。首先，我们建立了该算法在封闭系统中的线性收敛性，即估计值向极小点收敛的线性收敛性，适用于一般图和适当的步长。其次，我们估计替换后最优解的变化，以评估其对当前估计值与极小点之间距离的影响。基于这两个要素，我们推导出开放系统中的稳定性条件，并建立了该算法向稳态期望误差的线性收敛性。在局部函数光滑、强凸且其极小点位于给定球内的假设下，我们的结果能够刻画收敛速度与对智能体替换的鲁棒性之间的权衡。此外，本文提出的方法可以扩展到其他在封闭系统中保证线性收敛的算法。
英文摘要：
We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In particular, we characterize the evolution of the distance to the minimizer in expectation by following a time-varying optimization approach which builds on two components. First, we establish the linear convergence of the algorithm in closed systems, in terms of the estimate towards the minimizer, for general graphs and appropriate step-size. Second, we estimate the change of the optimal solution after a replacement, in order to evaluate its effect on the distance between the current estimate and the minimizer. From these two elements, we derive stability conditions in open systems and establish the linear convergence of the algorithm towards a steady-state expected error. Our results enable to characterize the trade-off between speed of convergence and robustness to agent replacements, under the assumptions that local functions are smooth, strongly convex, and have their minimizers located in a given ball. The approach proposed in this paper can moreover be extended to other algorithms guaranteeing linear convergence in closed system.
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