Abstract: Various gradient compression algorithms have been proposed to alleviate the communication bottleneck in distributed learning, and they have demonstrated effectiveness in terms of high compression ratios and theoretical low communication complexity. However, when it comes to practically training modern deep neural networks (DNNs), these algorithms have yet to match the inference performance of uncompressed SGD-momentum (SGDM) and adaptive optimizers (e.g.,Adam). More importantly, recent studies suggest that these algorithms actually offer no speed advantages over SGDM/Adam when used with common distributed DNN training frameworks ( e.g., DistributedDataParallel (DDP)) in the typical settings, due to heavy compression/decompression computation or incompatibility with the efficient All-Reduce or the requirement of uncompressed warmup at the early stage. For these reasons, we propose a novel 1-bit adaptive optimizer, dubbed *Bi*nary *r*andomization a*d*aptive optimiz*er* (**Birder**). The quantization of Birder can be easily and lightly computed, and it does not require warmup with its uncompressed version in the beginning. Also, we devise Hierarchical-1-bit-All-Reduce to further lower the communication volume. We theoretically prove that it promises the same convergence rate as the Adam. Extensive experiments, conducted on 8 to 64 GPUs (1 to 8 nodes) using DDP, demonstrate that Birder achieves comparable inference performance to uncompressed SGDM/Adam, with up to ${2.5 \times}$ speedup for training ResNet-50 and ${6.3\times}$ speedup for training BERT-Base. Code is publicly available at https://openi.pcl.ac.cn/c2net_optim/Birder.