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In this paper, we present a communication-efficient federated learningframework inspired by quantized compressed sensing. The presented frameworkconsists of gradient compression for wireless devices and gradientreconstruction for a parameter server (PS). Our strategy for gradientcompression is to sequentially perform block sparsification, dimensionalreduction, and quantization. Thanks to gradient sparsification andquantization, our strategy can achieve a higher compression ratio than one-bitgradient compression. For accurate aggregation of the local gradients from thecompressed signals at the PS, we put forth an approximate minimum mean squareerror (MMSE) approach for gradient reconstruction using theexpectation-maximization generalized-approximate-message-passing (EM-GAMP)algorithm. Assuming Bernoulli Gaussian-mixture prior, this algorithmiteratively updates the posterior mean and variance of local gradients from thecompressed signals. We also present a low-complexity approach for the gradientreconstruction. In this approach, we use the Bussgang theorem to aggregatelocal gradients from the compressed signals, then compute an approximate MMSEestimate of the aggregated gradient using the EM-GAMP algorithm. We alsoprovide a convergence rate analysis of the presented framework. Using the MNISTdataset, we demonstrate that the presented framework achieves almost identicalperformance with the case that performs no compression, while significantlyreducing communication overhead for federated learning.

Communication-Efficient Federated Learning via Quantized Compressed Sensing