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We consider the problem of decentralized consensus optimization, where thesum of $n$ smooth and strongly convex functions are minimized over $n$distributed agents that form a connected network. In particular, we considerthe case that the communicated local decision variables among nodes arequantized in order to alleviate the communication bottleneck in distributedoptimization. We propose the Quantized Decentralized Gradient Descent (QDGD)algorithm, in which nodes update their local decision variables by combiningthe quantized information received from their neighbors with their localinformation. We prove that under standard strong convexity and smoothnessassumptions for the objective function, QDGD achieves a vanishing mean solutionerror under customary conditions for quantizers. To the best of our knowledge,this is the first algorithm that achieves vanishing consensus error in thepresence of quantization noise. Moreover, we provide simulation results thatshow tight agreement between our derived theoretical convergence rate and thenumerical results.

An Exact Quantized Decentralized Gradient Descent Algorithm