通訊與訊號處理之分散式最佳化方法

分散式最佳化涵蓋許多如智慧電網、無線通訊與資料科學之應用，近來亦成為重要的研究目標。這些演算法時常應用於來自不同地點的資料收集與處理。儘管不同處理節點間之共識機制並非必要，本論文對於特定通訊與訊號處理問題，提出分散式最佳化之共識演算法。網路處理節點(或稱代理人)需在本研究如同集合體一般對所有當前觀測到的事件達到共識。在此情況下，資料通常座落於不規則的場域，處理節點(代理人)所形成之網路可以被模擬為象徵訊號、資訊網路以及實體網路的圖模型。「耦合性」為在進行最佳化問題描述階段會遇到的難點之一。亦即在其中一個節點上做計算需要其他節點的運算結果。本論文中透過通訊與訊號處理的不同應用凸顯不同種類的耦合。首先，協調式多點傳輸（JT-CoMP）的傳輸點選擇與預編碼器之聯合設計在設計當中納入了前傳限制，並兼顧了覆蓋區域。其中有兩個分散式演算法使得前述之協調式多點傳輸設計能隨系統規模而擴展;一個使用了交替方向乘子法（ADMM）而另一個使用了基於共識機制的近端對偶分解演算法。本論文亦提到分散式資料分群與非監督聯盟式學習的問題應用。分布式對偶平均法（DDA）提供了不需交換中心點的實際應用，將更適合於特定應用與處理網路節點中不平衡的資料分布。

關鍵字

分散式最佳化；無線通訊；訊號處理

並列摘要

Distributed optimization has recently been a subject of intensive research, with many applications such as smart grid, wireless communications, and data science. These algorithms are usually applied when data are collected and processed at different locations. While consensus among processing nodes is not necessary, in this work, distributed optimal consensus algorithms are developed for selected communications and signal processing problems, where the agents need to act as a collective and establish an agreement for all present events. In this case, the network of processing nodes, or agents, can be modeled as a graph, which can be used to represent signal and information network, as well as physical network, as in the case here, where data lie on an irregular structure. One of the main obstacles in formulating the optimization problem is to deal with emph{coupling}, where processing on one node requires result of others. Different kinds of coupling will be highlighted in this thesis through different applications in communications and signal processing. First, joint Joint Transmission-CoMP Transmission Point selection and precoder design is proposed that incorporates a fronthaul constraint as part of the design which allows for cooperating coverage areas. Two distributed algorithms are proposed to make the previous JT-CoMP design scalable, one using the Alternating Direction Method of Multipliers and the other uses consensus-based proximal-dual decomposition algorithm. Next, the problems of distributed data clustering and unsupervised federated learning are considered. A distributed dual averaging algorithms are proposed to provide practical design, that does not require exchange of the centroids, which is more suitable for certain applications and is able to unbalanced data distributed across nodes of the network.