# Communication-Efficient Federated Learning with Adaptive Consensus ADMM
## 1 Introduction  
The Internet of Things (IoT) has permeated many aspects of our daily lives through the proliferation of smart services and applications empowered by artificial intelligence (AI) [1]. HIS Markit estimates that by 2030, the number of IoT devices will reach 125 billion [2]. The massive number of IoT devices generates a huge amount of data that is aggregated by the industry in the cloud. Machine learning (ML) has evolved over the last few years as an effective methodology for handling complex data [3]. However, these IoT-generated data contain sensitive information about users or organizations, such as facial images, location information, health information, or fingerprint information. Uploading this information could result in information leakage. The issue of management and governance of data resources is the focus of many countries and government regulatory efforts. Countries and regions have introduced laws such as the General Data Protection Regulation (GDPR) [4] in the EU, the Personal Data Protection Act (PDP) [5] in Singapore, and the California Consumer Privacy Act (CCPA) [6] and the Consumer Privacy Bill of Rights (CPBR) [7] in the US to protect data privacy and security. This makes traditional centralized machine learning approaches, where distributed raw data generated on different devices or organizations are collected into a single server or a cluster with shared data storage, impossible. Federated Learning (FL) is a novel distributed machine learning framework that allows user devices to benefit from models trained on rich data without the need to centrally collect these data. This approach safeguards the privacy and security of users. Federated learning comprises two parts: the edge mobile device (also known as the client) and the central server. In federated learning, the learning task is accomplished by a decentralized federation of clients that participate in federated learning, and these devices are coordinated by a central server. Each dataset of a client is locally trained and is not uploaded to the central server. Simultaneously, each client computationally updates the global model downloaded from the central server and sends the updated model back to the central server. The basic process of FL is described in [8] and shown in Figure 1.  
First, the model is trained locally, and then the parameters of the model are sent to the server. Finally, the cloud server returns the aggregated model to the local device. The above steps are repeated throughout the federated learning process until convergence. FedAvg is a method of simply averaging the locally uploaded models on the server [8]. Practically, FedAvg does not perform well when dealing with the complicated diversity of devices and data in the real world. [PERSON] et al. [9] proposed a federated optimization, FedProx, which is used to settle heterogeneity in FL. FedProx improves stability by adding a proximal term to the local training subproblem on every local device. Unfortunately, such a method did not meet the needs of various applications and did not obtain an improvement in convergence speed. FedMA is a new layer-wise FL algorithm for modern CNNs and LSTMs that appeal to Bayesian nonparametric methods to adapt to heterogeneity in the data [10]. However, this statistics-oriented aggregation method is susceptible to model poisoning attacks. Primal-dual optimization method is a basic algorithm extensively employed in distributed learning. The alternating direction method of multipliers (ADMM) is a straightforward yet powerful approach that is particularly suitable for resolving distributed convex optimization issues, especially in the fields of applied statistics and machine learning [11]. ADMM takes on the shape of a decomposition-coordination technique, where solutions to small local subproblems are coordinated to discover solutions to large global problems. ADMM depends on a user-selected penalty parameter (step size) as its foundation.