We consider problems where agents in a network seek a common quantity, measured independently and periodically by each agent through a local time-varying process. Numerous solvers addressing such problems have been developed in the past, featuring various adaptations of the local processing and the consensus step. However, existing solvers still lack support for advanced techniques, such as superiorization and over-the-air function computation (OTA-C). To address this limitation, we introduce a comprehensive framework for the analysis of distributed algorithms by characterizing them using the quasi-Fej\'er type algorithms and an extensive communication model. Under weak assumptions, we prove almost sure convergence of the algorithm to a common estimate for all agents. Moreover, we develop a specific class of algorithms within this framework to tackle distributed optimization problems with time-varying objectives, and, assuming that a time-invariant solution exists, prove its convergence to a solution. We also present a novel OTA-C protocol for consensus step in large decentralized networks, reducing communication overhead and enhancing network autonomy as compared to the existing protocols. The effectiveness of the algorithm, featuring superiorization and OTA-C, is demonstrated in a real-world application of distributed supervised learning over time-varying wireless networks, highlighting its low-latency and energy-efficiency compared to standard approaches.

翻译：我们考虑网络中的智能体各自通过局部时变过程独立周期性地测量一个共同量的问题。过去已开发出多种解决此类问题的算法，这些算法对局部处理步骤和一致性步骤进行了各种改进。然而，现有算法仍不支持先进技术，如超优化和空中计算（OTA-C）。为解决这一局限，我们引入了一个综合分析分布式算法的框架，通过拟费耶尔型算法和扩展通信模型对算法进行刻画。在弱假设条件下，我们证明了算法几乎必然收敛到所有智能体的共同估计量。此外，我们在此框架内开发了一类特定算法以处理具有时变目标的分布式优化问题，并在假设存在时不变解的情况下，证明了其收敛到解。我们还针对大规模去中心化网络中的一致性步骤提出了一种新型OTA-C协议，与现有协议相比，该协议降低了通信开销并增强了网络自主性。在时变无线网络上的分布式监督学习实际应用中，我们展示了融合超优化和OTA-C的算法有效性，突显了其相比标准方法的低延迟和高效能特点。