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The proliferation of the Internet of Things (IoT) and widespread use of devices with sensing, computing, and communication capabilities have motivated intelligent applications empowered by artificial intelligence. The classical artificial intelligence algorithms require centralized data collection and processing which are challenging in realistic intelligent IoT applications due to growing data privacy concerns and distributed datasets. Federated Learning (FL) has emerged as a distributed privacy-preserving learning framework that enables IoT devices to train global model through sharing model parameters. However, inefficiency due to frequent parameters transmissions significantly reduce FL performance. Existing acceleration algorithms consist of two main type including local update considering trade-offs between communication and computation and parameter compression considering trade-offs between communication and precision. Jointly considering these two trade-offs and adaptively balancing their impacts on convergence have remained unresolved. To solve the problem, this paper proposes a novel efficient adaptive federated optimization (EAFO) algorithm to improve efficiency of FL, which minimizes the learning error via jointly considering two variables including local update and parameter compression and enables FL to adaptively adjust the two variables and balance trade-offs among computation, communication and precision. The experiment results illustrate that comparing with state-of-the-art algorithms, the proposed EAFO can achieve higher accuracies faster.