With the increasing number of smart devices and the development of machine learning technology, the value of users' personal data is becoming more and more important. Based on the premise of protecting users' personal privacy data, federated learning (FL) uses data stored on edge devices to realize training tasks by contributing training model parameters without revealing the original data. However, since FL can still leak the user's original data by exchanging gradient information. The existing privacy protection strategy will increase the uplink time due to encryption measures. It is a huge challenge in terms of communication. When there are a large number of devices, the privacy protection cost of the system is higher. Based on these issues, we propose a privacy-preserving scheme of user-based group collaborative federated learning (GrCol-PPFL). Our scheme primarily divides participants into several groups and each group communicates in a chained transmission mechanism. All groups work in parallel at the same time. The server distributes a random parameter with the same dimension as the model parameter for each participant as a mask for the model parameter. We use the public datasets of modified national institute of standards and technology database (MNIST) to test the model accuracy. The experimental results show that GrCol-PPFL not only ensures the accuracy of the model, but also ensures the security of the user's original data when users collude with each other. Finally, through numerical experiments, we show that by changing the number of groups, we can find the optimal number of groups that reduces the uplink consumption time.

Federated Learning (FL) is a distributed machine learning framework to alleviate the data silos, where decentralized clients collaboratively learn a global model without sharing their private data. However, the clients' Non-Independent and Identically Distributed (Non-IID) data negatively affect the trained model, and clients with different numbers of local updates may cause significant gaps to the local gradients in each communication round. In this paper, we propose a Federated Vectorized Averaging (FedVeca) method to address the above problem on Non-IID data. Specifically, we set a novel objective for the global model which is related to the local gradients. The local gradient is defined as a bi-directional vector with step size and direction, where the step size is the number of local updates and the direction is divided into positive and negative according to our definition. In FedVeca, the direction is influenced by the step size, thus we average the bi-directional vectors to reduce the effect of different step sizes. Then, we theoretically analyze the relationship between the step sizes and the global objective, and obtain upper bounds on the step sizes per communication round. Based on the upper bounds, we design an algorithm for the server and the client to adaptively adjusts the step sizes that make the objective close to the optimum. Finally, we conduct experiments on different datasets, models and scenarios by building a prototype system, and the experimental results demonstrate the effectiveness and efficiency of the FedVeca method.