We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization problem called sample quantile inference, which we solve using a two-time-scale stochastic approximation algorithm. Herein, we prove the algorithm's convergence in the almost sure sense to an optimal solution. Moreover, our algorithm handles noise and empirically converges to the correct answer within a small number of iterations.

翻译：我们考虑从一个由美元代理商组成的网络中分布的、有噪音通信连接的数据集中,确定最高至1千美元的最大测量数据的问题。我们表明,这一假设情景可以被描绘成一个分布式的二次曲线优化问题,称为四分位数抽样推断,我们用两个尺度的随机近似算法来解决。在这里,我们证明算法几乎可以肯定地与最佳解决办法相融合。此外,我们的算法处理噪音,在经验上与少数迭代的正确答案相融合。