对动态多智能体网络提出对数量化优化，提升近优解精度。
Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks
- 采用对数量化机制，小值用更多比特表示，大值用更少比特。
- 在动态网络下实现收敛，近优解精度优于均匀量化。
- 适合带宽受限的分布式机器学习与控制场景。
分布式优化广泛应用于机器学习、信号处理和控制系统。在实际应用中，通信网络的带宽限制要求采用量化技术。本文提出一种在多智能体网络中基于对数量化数据传输的分布式优化动态方法。该方法使小数值使用更多比特表示，大数值使用较少比特，相比均匀量化能更精确表示接近最优的解，从而提高算法准确性。所提优化动态包含一个收敛至最优解的状态变量和一个跟踪目标函数梯度的辅助变量。该设置支持动态网络拓扑，构成混合系统，需借助矩阵扰动理论与特征谱分析进行收敛性证明。
原文摘要 · Abstract (English)
Distributed optimization finds many applications in machine learning, signal processing, and control systems. In these real-world applications, the constraints of communication networks, particularly limited bandwidth, necessitate implementing quantization techniques. In this paper, we propose distributed optimization dynamics over multi-agent networks subject to logarithmically quantized data transmission. Under this condition, data exchange benefits from representing smaller values with more bits and larger values with fewer bits. As compared to uniform quantization, this allows for higher precision in representing near-optimal values and more accuracy of the distributed optimization algorithm. The proposed optimization dynamics comprise a primary state variable converging to the optimizer and an auxiliary variable tracking the objective function's gradient. Our setting accommodates dynamic network topologies, resulting in a hybrid system requiring convergence analysis using matrix perturbation theory and eigenspectrum analysis.
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