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In this paper, we focus on a popular DML framework -- the parameter servercomputation paradigm and iterative learning algorithms that proceed in rounds.We aim to reduce the communication complexity of Byzantine-tolerant DMLalgorithms in the single-hop radio network. Inspired by the CGC filterdeveloped by Gupta and Vaidya, PODC 2020, we propose a gradient descent-basedalgorithm, Echo-CGC. Our main novelty is a mechanism to utilize the broadcastproperties of the radio network to avoid transmitting the raw gradients (full$d$-dimensional vectors). In the radio network, each worker is able to overhearprevious gradients that were transmitted to the parameter server. Roughlyspeaking, in Echo-CGC, if a worker "agrees" with a combination of priorgradients, it will broadcast the "echo message" instead of the its raw localgradient. The echo message contains a vector of coefficients (of size at most$n$) and the ratio of the magnitude between two gradients (a float). Incomparison, the traditional approaches need to send $n$ local gradients in eachround, where each gradient is typically a vector in an ultra-high dimensionalspace ($d\gg n$). The improvement on communication complexity of our algorithmdepends on multiple factors, including number of nodes, number of faultyworkers in an execution, and the cost function. We numerically analyze theimprovement, and show that with a large number of nodes, Echo-CGC reduces$80\%$ of the communication under standard assumptions.

Echo-CGC: A Communication-Efficient Byzantine-tolerant Distributed Machine Learning Algorithm in Single-Hop Radio Network