In this paper, a novel distributed stochastic approximation algorithm (DSAA) is proposed to seek roots of the sum of local functions, each of which is associated with an agent from multiple agents connected over a network. At each iteration, each agent updates its estimate for the root utilizing the noisy observations of its local function and the information derived from the neighboring agents. The key difference of the proposed algorithm from the existing ones consists in the expanding truncations (so it is called the DSAAWET), by which the boundedness of the estimates can be guaranteed without imposing the growth-rate constraints on the local functions. The estimates generated by the DSAAWET are shown to converge almost surely to a consensus set, which belongs to a connected subset of the root set of the sum function. In comparison with the existing results, we impose weaker conditions on the local functions and on the observation noise. We then apply the proposed algorithm to two applications, one from signal processing and the other one from distributed optimization, and establish the almost sure convergence. Numerical simulation results are also included.

中文翻译：

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具有扩展截断的分布式随机逼近算法

在本文中，提出了一种新颖的分布式随机逼近算法 (DSAA) 来寻找局部函数总和的根，每个局部函数都与来自通过网络连接的多个代理的代理相关联。在每次迭代中，每个代理利用其局部函数的噪声观察和从相邻代理得出的信息更新其对根的估计。所提出的算法与现有算法的主要区别在于扩展截断（因此称为 DSAAWET），通过它可以保证估计的有界性，而无需对局部函数施加增长率约束。由 DSAAWET 生成的估计显示几乎肯定会收敛到一个共识集，它属于和函数的根集的连接子集。与现有结果相比，我们对局部函数和观测噪声施加了较弱的条件。然后我们将所提出的算法应用于两种应用，一种来自信号处理，另一种来自分布式优化，并建立几乎肯定的收敛性。数值模拟结果也包括在内。