[论文解读] Accelerated Hierarchical ADMM for Nonconvex Optimization in Multi-Agent Decision Making.

Xiaoxue Zhang, Jun Ma+4 more|arXiv (Cornell University)|Nov 1, 2020

Distributed Control Multi-Agent Systems被引用 4

一句话总结

本文提出一种带有障碍加速的分层三块ADMM方法，用于求解多智能体系统中的非凸分布式优化问题，特别适用于无人机决策。通过引入松弛变量，并将外层ALM与内层半近端ADMM相结合，该方法实现了对驻点的收敛，且在计算效率上显著优于标准方法。

ABSTRACT

Distributed optimization is widely used to solve large-scale problems effectively in a localized and coordinated manner. Thus, it is noteworthy that the methodology of distributed model predictive control (DMPC) has become a promising approach to achieve effective outcomes; and particularly in decision-making tasks for multi-agent systems. However, the typical deployment of such DMPC frameworks would lead to involvement of nonlinear processes with a large number of nonconvex constraints. Noting all these attendant constraints and limitations, the development and innovation of a hierarchical three-block alternating direction method of multipliers (ADMM) approach is presented in the work here to solve the nonconvex optimization problem that arises for such a decision-making problem in multi-agent systems. Firstly thus, an additional slack variable is introduced to relax the original large-scale nonconvex optimization problem; such that the intractable nonconvex coupling constraints are suitably related to the distributed agents. Then, the approach with a hierarchical ADMM that contains outer loop iteration by the augmented Lagrangian method (ALM), and inner loop iteration by three-block semi-proximal ADMM, is utilized to solve the resulting relaxed nonconvex optimization problem. Additionally, it is shown that the appropriate desired stationary point exists for the procedures of the hierarchical stages for convergence in the algorithm. Next, the approximate optimization with a barrier method is then applied to accelerate the computational efficiency. Finally, a multi-agent system involving decision-making for multiple unmanned aerial vehicles (UAVs) is utilized to demonstrate the effectiveness of the proposed method in terms of attained performance and computational efficiency.

研究动机与目标

• 解决具有耦合约束的大规模非凸优化问题在多智能体决策中的挑战。
• 克服分布式模型预测控制（DMPC）框架中非凸耦合约束带来的计算不可行性。
• 开发一种可扩展且收敛的非凸优化算法，支持分布式智能体协调。
• 通过在分层ADMM框架中引入障碍方法加速，提升计算效率。
• 在真实世界的多无人机决策场景中验证该方法的有效性。

提出的方法

• 引入松弛变量以松弛原始的非凸优化问题，将难以处理的耦合约束转化为可分布式处理的组件。
• 采用分层ADMM结构，外层使用增广拉格朗日法（ALM）以保证全局收敛性。
• 在内层采用三块半近端ADMM，以分布式方式求解松弛后的子问题。
• 应用近似障碍方法以加速收敛，并在优化过程中提升计算效率。
• 通过算法结构设计与适当的步长选择，确保收敛至驻点。
• 将问题在智能体间分解，使每个智能体求解本地子问题，同时通过对偶变量和一致性约束进行协调。

实验结果

研究问题

• RQ1 带有三块更新的分层ADMM框架能否在多智能体系统的非凸分布式优化中实现收敛？
• RQ2 引入松弛变量如何提升分布式决策中非凸耦合约束的可处理性？
• RQ3 在所提出的ADMM框架中，障碍方法近似对计算速度和解的质量有何影响？
• RQ4 尽管存在非凸性与分布式协调，该算法在多大程度上仍能保持收敛保证？
• RQ5 该方法在真实世界多智能体场景（如无人机编队控制）中的表现如何？

主要发现

• 在给定的算法结构下，所提出的带有ALM与半近端更新的分层ADMM可收敛至驻点。
• 引入松弛变量成功解耦了非凸耦合约束，使分布式求解过程成为可能。
• 障碍方法近似显著加速了收敛，提升了计算效率，且未牺牲解的质量。
• 该方法在多无人机决策场景中表现出色，实现了高质量解与快速计算的双重优势。
• 该算法在非凸性和大规模问题条件下仍保持稳定与收敛，适用于多智能体系统中常见的复杂场景。