A Communication-Efficient Distributed Optimization Algorithm with Linear Convergence over Directed Graphs

The Industrial Internet of Things (IIoT) is increasingly emerging as a novel paradigm for information exchange within industrial production environments. To facilitate the efficient operation of IIoT, there is an urgent requirement for communication-efficient methods to transmit extensive production data. This paper proposes a communication-efficient distributed optimization algorithm tailored for the strongly convex and smooth convex optimization problems over a directed graph. To encompass a broader class of compressors, the assumption of compressor is relaxed to contain both relative and absolute errors. To mitigate compression errors, we adopt differential compression technique and dynamic scaling factor in the algorithm. In particular, under this compression assumption, a non-uniform quantizer is introduced to enable finite-bit transmission over communication channels and an upper bound of the required bits with this quantizer is provided. Moreover, we prove the linear convergence of the proposed algorithm with compression, and numerical examples are provided to verify the performance of the proposed algorithm.