Communication of model updates between client nodes and the central\naggregating server is a major bottleneck in federated learning, especially in\nbandwidth-limited settings and high-dimensional models. Gradient quantization\nis an effective way of reducing the number of bits required to communicate each\nmodel update, albeit at the cost of having a higher error floor due to the\nhigher variance of the stochastic gradients. In this work, we propose an\nadaptive quantization strategy called AdaQuantFL that aims to achieve\ncommunication efficiency as well as a low error floor by changing the number of\nquantization levels during the course of training. Experiments on training deep\nneural networks show that our method can converge in much fewer communicated\nbits as compared to fixed quantization level setups, with little or no impact\non training and test accuracy.\n