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：摘要：本文考虑网络中智能体通过本地时变过程各自独立周期性地测量某一共同量的优化问题。现有研究已开发出多种求解此类问题的算法，通过对本地处理步骤与一致性步骤进行不同改进。然而，现有求解器仍缺乏对先进技术（如超优化与空中函数计算（OTA-C））的支持。为弥补这一不足，我们提出一个用于分析分布式算法的通用框架，通过准费耶尔型算法与广义通信模型对算法进行刻画。在弱假设条件下，我们证明算法几乎必然收敛至所有智能体的共同估计值。进一步地，我们在该框架内设计了一类特定算法以求解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前提下，证明其收敛至某一解。此外，我们提出一种适用于大规模去中心化网络的新型OTA-C一致性协议，与现有协议相比，该协议可降低通信开销并增强网络自主性。在时变无线网络上的分布式监督学习实际应用中，我们特别展示了结合超优化与OTA-C的算法有效性，并突出其相较于标准方法的低延迟与高能效特性。