Gradient compression with error compensation has attracted significant attention with the target of reducing the heavy communication overhead in distributed learning. However, existing compression methods either perform only unidirectional compression in one iteration with higher communication cost, or bidirectional compression with slower convergence rate. In this work, we propose the Local Immediate Error Compensated SGD (LIEC-SGD) optimization algorithm to break the above bottlenecks based on bidirectional compression and carefully designed compensation approaches. Specifically, the bidirectional compression technique is to reduce the communication cost, and the compensation technique compensates the local compression error to the model update immediately while only maintaining the global error variable on the server throughout the iterations to boost its efficacy. Theoretically, we prove that LIEC-SGD is superior to previous works in either the convergence rate or the communication cost, which indicates that LIEC-SGD could inherit the dual advantages from unidirectional compression and bidirectional compression. Finally, experiments of training deep neural networks validate the effectiveness of the proposed LIEC-SGD algorithm.
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