Quantized Zeroth-Order Gradient Tracking Algorithm for Distributed Nonconvex Optimization Under Polyak–Łojasiewicz Condition
本文提出一种量化分布式零阶算法，结合确定性梯度估计、均匀量化器和梯度跟踪，在Polyak–Łojasiewicz条件下实现线性收敛，适用于通信带宽受限且梯度不可用的场景。
This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak-Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.