An Exact Quantized Decentralized Gradient Descent Algorithm
This addresses communication bottlenecks in distributed optimization for networked agents, representing an incremental improvement by introducing quantization to existing methods.
The paper tackles decentralized consensus optimization with quantized communication to reduce bandwidth, proposing the QDGD algorithm that achieves vanishing mean solution error under strong convexity and smoothness assumptions, with simulation results confirming the theoretical convergence rate.
We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for the objective function, QDGD achieves a vanishing mean solution error under customary conditions for quantizers. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the numerical results.