多智能体网络中的高效分布式一致优化算法研究

Decentralized consensus optimization is an important research topic in multi-agent networks and has wide applications in network optimization, control, and data analytics. Without the aid of any fusion center, in decentralized consensus optimization algorithms nodes exchange information among neighbors, utilize local data, and autonomously optimize an overall objective function of the whole network. Currently, theoretical foundations of decentralized consensus optimization problem are still far from established. In particular, communication efficiency and computation efficiency, which are two key issues in algorithm design, are not well studied. This project aims to investigate design and analysis of decentralized consensus optimization algorithms that are efficient in terms of communication and computation. Detailed research topics and innovations are three fold. First, we analyze the optimal convergence rate of decentralized first-order algorithms, as well as design and implement the Nesterov acceleration technique in multi-agent networks. Second, based on the considerations of communication cost and computation cost, we design efficient decentralized algorithms from four perspectives, including quantized communications, asynchronization schemes, approximately solving subproblems, and handling composite local objective functions; through investigating the tradeoff between computation cost and communication cost, we provide a guideline to designing multi-agent networks in which agents have different levels of resources. Third, we validate the effectiveness of algorithmic design and theoretical analysis on an experimental wireless sensor network through handling an event detection task, which can be formulated as a decentralized sparse optimization problem.

分布式一致优化是多智能体网络中的重要问题，在网络优化、控制、数据处理等领域有着广泛的应用。在分布式一致优化算法中，节点无需融合中心，借助邻居间的信息交换，利用本地数据，自主的优化网络的整体目标函数。目前，分布式一致优化问题的理论基础尚未完善，对算法设计中通信效率与计算效率两个关键问题的研究尚未深入。本项目拟研究通信高效、计算高效的分布式一致优化算法的设计与分析，研究内容与创新点为：（1）分析分布式一阶算法的最优收敛速度，研究多智能体网络中Nesterov加速技术的设计与实现；（2）以通信代价与计算代价两个问题为核心，从量化通信、异步机制、子问题近似求解、可分本地目标函数处理四个角度，设计高效的分布式算法，研究计算代价与通信代价的折中，指导适合不同类型多智能体网络的设计；（3）针对基于无线传感器网络的事件检测这一分布式稀疏优化问题，在无线传感器网络实验平台上验证算法设计与理论分析的有效性。

分布式一致优化是多智能体网络中的重要问题，在网络优化、控制、数据处理等领域有着广泛的应用。在分布式一致优化算法中，节点无需融合中心，借助邻居间的信息交换，利用本地数据，自主的优化网络的整体目标函数。目前，分布式一致优化问题的理论基础尚未完善，对算法设计中通信效率与计算效率两个关键问题的研究尚未深入。本项目拟研究通信高效、计算高效的分布式一致优化算法的设计与分析，研究内容与创新点为：（1）分析分布式一阶算法的最优收敛速度，研究多智能体网络中Nesterov加速技术的设计与实现；（2）以通信代价与计算代价两个问题为核心，从量化通信、异步机制、子问题近似求解、可分本地目标函数处理四个角度，设计高效的分布式算法，研究计算代价与通信代价的折中，指导适合不同类型多智能体网络的设计；（3）针对基于无线传感器网络的事件检测这一分布式稀疏优化问题，在无线传感器网络实验平台上验证算法设计与理论分析的有效性。.在本项目的支持下，研究组对多智能体网络中的一致优化问题进行了深入的研究，取得了一系列重要成果，包括：（1）首次证明了经典的分布式梯度下降法具有近似线性收敛性，为分布式一阶算法的收敛速度分析奠定了基础；（2）基于通信删失技术开发了一系列通信高效的分布式优化算法；（3）基于二阶方法与邻近点梯度法开发了一系列计算高效的分布式优化算法；（4）开发并分析了异步、时延情况下的分布式优化算法；（5）研究了分布式优化算法在网络资源分配中的应用。