Alternating direction method of multipliers (ADMM) has recently been identified as a compelling approach for solving large-scale machine learning problems in the cluster setting. To reduce the synchronization overhead in a distributed environment, asynchronous distributed ADMM (AD-ADMM) was proposed. However, due to the high communication overhead in the master-slave architecture, AD-ADMM still cannot scale well. To address this challenge, this paper proposes the ADMMLIB, a library of AD-ADMM for distributed machine learning. We employ a set of network optimization techniques. First, hierarchical communication architecture is utilized. Second, we integrate ring-based allreduce and mixed precision training into ADMMLIB to further effectively reduce the inter-node communication cost. Evaluation with large dataset demonstrates that ADMMLIB can achieve significant speed up, up to 2x, compared to the original AD-ADMM implementation, and the overall communication cost is reduced by 83%.