With the rapid development of the national power grid, the demand for efficient and reliable power supply is increasing. As the labor cost and the size of the power grid are increasing, the Unmanned Aerial Vehicle (UAV) power inspection is a new and efficient way of detecting power grid abrasion. By analyzing the data collected by the UAVs, a smart detection and maintenance service can be provided. To improve the model robustness and accuracy, data collected from different companies and regions are required, which may violate the data privacy policy. As a distributed machine learning technique, Federated Learning (FL) can collaboratively train global models without sharing private data. In this article, in order to protect the data privacy between different systems, optimize models' accuracy and convergence performance for non-Independently-and-Identically-Distributed (non-IID) data, we propose an adaptive method that jointly adjusts the learning rate and gradient based on the idea of FL. By recording global gradient information and using the momentum to accelerate the training process, our method adaptively controls the local gradient and learning rate in training of local models, and be more robust to local minima. Finally, we verify the superiority of our model compared with the generic FL model for nonIDD data through experiments.
model parameters and intermediate results without exposing the local source data to each other. FL approaches a unique way to balance the data sharing and data privacy protection, making data "available but not visible".
In previous distributed models, it is often assumed that the participants had Independently-andIdentically-Distributed (IDD) dataset. However, such an ideal scenario is often not available in most realistic scenarios. Participants are usually quite different from each other, as whose data are often non-IDD in practical questions. For example, in the power grid distributed across provinces, the climate in different regions causes different losses to cables. It also indicates that the server and participants need to communicate and exchange more times to achieve the required model accuracy. Unsatisfactory convergence performance, high communication cost and privacy guarantee also pose challenges to the optimization of FL’s non-IDD training model.
In the current research of FL, many training methods for models based on non-IDD data have been
proposed. FedAVG [
In response to this problem, some adaptive federated optimization methods have attracted
extensive attention. [
All related works list above extend our research ideas, nevertheless, few articles discuss the direction of integrated adaptive optimization of learning rate and gradient. In the training of deep learning network, the gradient and learning rate are both factors of great significance. The convergence performance of the model will be greatly improved theoretically by adapting them in local training and global aggregation. More specific method will be presented in next section. 2.
Federated Learning (FL) was approached by B. McMahan et al. in 2016 as a decentralized
machine learning mechanism [
FedAVG algorithm is a classical federated learning algorithm [
In each communication round, the client uses its source data locally to perform one-step gradient descent on the current model to obtain the model parameters of the client: where is the gradient at iteration
of client , is the learning rate of the model. After receiving local parameters, servers perform model average operation to update global parameters:
The updated global parameters are synchronized to all clients for the next round of local training, and the process is repeated (Show in Figure 1).
Compared with the generic FedSGD model, the Fe-dAVG algorithm is much more accurate and
robust to non-IID data to a certain extent. However, as it adopts static learning rate, gradient and other
parameters in local training, its convergence speed will still be slow in the case of more imbalanced
non-IDD data in practical problems. There is still room for its improvement in this case [
Recent times, the idea of adaptively updating static parameters has spawned many optimization
methods of FL, which can achieve faster convergence on non-IDD datasets while ensuring robustness.
FedADAM [
Communication cost plays a dominant role in the optimization of federated learning. We consider reducing the number of communication rounds required for training the model by using additional computation, so as to achieve faster convergence. Therefore, we refer to FedADAM algorithm and propose a new adaptive method according to the idea of dynamic adjustment of static parameters such as learning rate and gradient.
The pseudocode of the Algorithm is presented in Algorithm 1 and abstractly show in Figure 2:
Algorithm 1 shows our adaptive approach, is the fraction of clients participating in each round, is the set of all clients, are hyperparameters of the model which could be customize before training, denotes the learning rate. Therefore, clients are sampled at the beginning of each global iteration. Assume the local parameter that the -th involved client received as , in each iteration the global parameter is transferred thus is assigned as: , where , where
Since the historical gradient information hasn’t been recorded in the first global iteration, the gradient of the loss function would be applied as the replacement of estimated local gradient function in the first epoch
: As the gradient of the loss function of participated clients differ from each other, which leads to a situation that FedAVG may have more divergent results and poor convergence when it performs multiple local updates for non-IDD dataset. To mitigate the unstable convergence performance of the model for non-IDD data in practical problems, the model could be adaptively adjusted by introducing the estimated gradient function, which enables the model to achieve better results for non-IDD data after multiple local updates in the correct update direction. After the first local update, the central server calculates estimated global gradient function with the global parameters of current and the previous global iterations as:
where , which will be delivered to the participated clients in the next global iteration for the update of the estimated gradient function of client at the remaining global iterations:
As shown in Algorithm 1, the core idea of our adaptive method is to perform the update of in each epoch of client
as follows: where is the gradient of the loss function with the local dataset at each epoch, is a hyper-parameter that we preset for adjusting . Then the update of local parameters at each epoch can be formulated as:
In addition, in order to accelerate the convergence speed and improve the performance of the
model for non-IDD data, -th epoch value of local parameters would be used to calculate
according to the idea of Adam [
During the aggregation phase, the central server receives the parameters and afinvolved clients, and aggregates their values to calculate the weighted Figure 3 Testing accuracy of FedAVG, FedADAM, Our Adaptive Method over MNIST dataset, with non-IDD,IDD data Figure 4 Testing accuracy of FedAVG, FedADAM, Our Adaptive Method over CIFAR-10 dataset, with non-IDD data parameters of the involved clients, which can be formulated as:
their values to calculate the weighted average of the local parameters of the involved clients, which can be formulated as:
At the end of each global iteration, the first moment estimation and second moment estimation are calculated with Adam’s method, and finally the global parameters is updated by: Such a design has the following advantages: a) Source Data in most of the practical problems (e.g. Electric power inspection with UAV System in our background) is often distributed inconsistently, which makes the model trained at the case of non-IDD data. By utilizing the global gradient information to adaptively update local parameter, faster and more robust convergence can be achieved.
b) According to the idea of FedADAM, we calculated the moment estimation using gradient information recorded in the history to adaptively regulate learning rate of training. It should receive much better effect in accelerating network training and inhibiting data oscillations.
c) The adaptive adjustment of parameters such as gradient and learning rate does not involve direct transmission of source data, which ensures data privacy of participants in federated learning.
d) Our adaptive adjustment focuses on the optimization in case of non-IDD data, in which participated clients can obtain more stable parameters through more local training. Through this way, the whole model is more inclined to train on the client side, which will greatly reduce the communication rounds and lower the cost of communication between the server and client. 3.
In the following, we will compare Our Adaptive Method, FedAVG and FedADAM to show the superiority of Our Method under local multi-epoch training.
There is no publicly available data about the electric power inspection with UAV on the Internet at
present. Without loss of generality, we selected MNIST [
In the experiment, we set the learning rate , and set for local update of Method can achieve the expected result.
By analyzing the results of the algorithm, the following conclusions can be obtained: a) For IDD data and implementing only one local training, the performance of Our Adaptive Method is not necessarily better than generic FedAVG and FedADAM, or even more mediocre. The reason is the main purpose of our adaptive improvement is to optimize the convergence speed and robustness of the model under the condition of non-IDD data. To save communication cost, more local training epochs is required to run on client. Under this circumstance, this method can truly attribute much faster and robust convergence with non-IDD data and significantly reduce the communication cost between server and client at the meantime, which is more meaningful in solving practical problems.
b) As the local epochs gradually increase, it can be observed that both FedAVG and FedADAM slow down the convergence speed to different degrees, while Our Adaptive Method keeps stable convergence performance. This is because there are often large differences between local data among participants for non-IID dataset. If the participated clients have gone through local updates for many times, the differences between participating clients will become larger and larger, thus the convergence efficiency will slow down a lot during server aggregation. However, Our Adaptive Method ensures higher accuracy and faster convergence speed through adaptive adjustment of parameters in this case.
In this article, we propose an adaptive FL method by using the momentum and adaptive gradient to optimize the convergence performance of the model. To achieve fast convergence, we introduce the new local gradient by considering the difference between the local gradient and historical global gradient. Furthermore, by tracking the first and second moment estimation of the gradients for model parameter, our algorithm adjusts the learning rate adaptively. At last, we perform simulation experiments using MNIST dataset and CIFAR-10 dataset to verify that our model can achieve faster convergence speed and higher accuracy than the widely used FL algorithm for non-IDD data. It is of great significance to accelerate the convergence of the model and reduce the communication cost in the practical problems of imbalanced data distribution.
This paper is funded by the Innovation and Entrepreneurship Training Program for College Students of Sun Yat-sen University. (Project number: 202211500)