Abstract Distributed adaptation over multitask networks has attracted particular attention due to its enhanced modeling capacity compared to that over conventional single-task networks. Most of the existing works derive their multitask adaptive algorithms using mean-square error (MSE) or least squares (LS) criterion, leading to multitask LMS- or LS-type algorithms. These algorithms, however, may suffer from deteriorated convergence rate or even divergence in impulsive noise environments. In order to address this problem, we propose a robust diffusion affine projection sign algorithm for multitask parameter estimation. The algorithm is derived by using the method of data reusing and minimizing the weighted sum of the l1-norms of some intermediate error vectors plus a similarity term subject to constraints on intermediate weight vectors at each agent. The multitask similarity relationship is characterized by the distance regularization among weight vectors. Furthermore, a variant of this algorithm, which is obtained by further regularizing the cost function by the l0-norm of the intermediate weight vector at each agent, is presented to promote convergence rate for jointly sparse parameter vectors estimation.

中文翻译：

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用于分布式估计的多任务扩散仿射投影符号算法及其稀疏变体

摘要 与传统的单任务网络相比，多任务网络上的分布式适应由于其增强的建模能力而受到特别关注。大多数现有工作使用均方误差 (MSE) 或最小二乘法 (LS) 准则推导出其多任务自适应算法，从而导致多任务 LMS 或 LS 型算法。然而，这些算法在脉冲噪声环境中可能会出现收敛速度变差甚至发散的问题。为了解决这个问题，我们提出了一种用于多任务参数估计的鲁棒扩散仿射投影符号算法。该算法是通过使用数据重用和最小化一些中间误差向量的 l1 范数的加权和加上一个受每个代理的中间权重向量约束的相似项的方法得出的。多任务相似关系的特点是权重向量之间的距离正则化。此外，该算法的一种变体是通过通过每个代理的中间权重向量的 l0 范数进一步正则化成本函数而获得的，以提高联合稀疏参数向量估计的收敛速度。