# Communication-Efficient Federated Learning with Adaptive Consensus ADMM
## 6 Conclusions  
In this paper, we discuss a practical scenario for federated learning that is characterized by a large number of clients with heterogeneous data and limited participation constraints. This scenario poses a challenge for achieving satisfactory convergence and model performance. To address this problem, we propose FedACADMM, a new federated objective optimization algorithm inspired by the adaptive consensus ADMM strategy in distributed optimization. Our proposed approach minimizes the communication cost per round, requiring storing additional variables at each client. This leads to a significant speed improvement as compared to the state-of-the-art model while reducing communication costs. We conducted extensive experiments on realistic datasets, and the results demonstrate that the algorithm is suitable for joint learning scenarios involving a large number of clients with heterogeneous data and limited participation constraints. Furthermore, the proposed algorithm exhibits good robustness and resilience and can achieve the target accuracy faster than the original methods while improving communication efficiency.  
Federated learning has gained significant attention due to its privacy-preserving effect, achieved by uploading only the model without the raw data, and it is a rapidly growing research area. Recently, there has been increasing interest in characterizing the convergence  
Figure 8: (**a**) Change in the global step-size \(\eta\) at the initial variable parameter \(\rho^{0}=10^{-3}\). In order to better show convergence, some train loss curves with poor performance are not shown. Additionally, we use the performance of \(\{\rho=10^{-2},\eta=1\}\) as a reference line. All experiments were performed in the 1000-client and non-IID data distributions setting on FMNIST. (**b**) Change in the global step-size \(\eta\) at the initial variable parameter \(\rho^{0}=10^{-2}\). All experiments were performed in the 1000-client and non-IID data distributions setting on FMNIST.  
rate of both centralized and distributed implementations of ADMM. In optimizing communication efficiency, the trade-off between reduced communication and accuracy is a critical focus of federated learning. The two most commonly studied solutions in federated optimization are bulk synchronous approaches and asynchronous approaches, where the delay is assumed to be bounded. In this paper, we only considered the bulk synchronous approach. However, in the future, we plan to consider more realistic device-centric communication schemes where each device can decide to communicate with the central server at its convenience, i.e., the asynchronous update approach.  
Conceptualization and writing--original draft preparation, S.H.; supervision, J.Z.; writing--review and editing, M.F. and Y.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China grant number 61761004.  
Not applicable.  
The data presented in this study are openly available in reference number [36,37].  
The authors declare no conflict of interest.