## 2 Federated Learning in AQI Prediction  
FL is training a ML model with cooperation between many participants (terminals or organizations, hereinafter referred to as clients) participating simultaneously without sharing data. At each training round, clients received global model parameters and perform local training with their data. Then clients return model parameters to aggregate a global model according to the Formula (1) [42; 43]. \[min\ F(w),where\ F(w):=\sum_{k=1}^{m}\ (p_{k}F_{k}(w)) \tag{1}\]  
\[and\ F_{k}(w)=\frac{1}{n_{k}}\sum_{k=1}^{n_{k}}(w;x_{j_{k}},y_{j_{k}}) \tag{2}\]  
where:  
\(m\): number of participants  
\(p_{k}\geq 0\) and \(\sum_{k}pk=1\)  
\(F_{k}\): Local optimization function on participant k in Formula (2)  
\(n_{k}\): number of data samples  
When the clients are terminal devices (mobiles, computers, Unmanned Aerial Vehicles or UAVs for short...) we call this relationship cross-devices, and cross-silos when the clients are organizations (hospitals, banks, schools...) [44]. The communication between clients is established in the following architecture: centralized, decentralized and hierarchy [45]. In addition, this architecture can also be classified according to the distributed data design of the system, including: Vertical FL, Horizontal FL and Transfer FL [46]. Since 2020, a few authors have investigated the use of FL in AQI prediction [47; 48; 49; 50; 51] or data missing prepossessing [52] for this task. Most authors agreed that FL outperformed the traditional ML methods in their research. Table 2 gives an overview of these works. Extending LSTM model in [47] to CNN-LSTM, [PERSON], et al. [48] developed a PSO-based method that uses UAVs swarm intelligence to identify the city's most dangerous zone. A plan for using UAV swarms to detect the quality of the air in the sky is put forth. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
\begin{tabular}{} \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Federated learning methods in AQI forecast. The suggested solution uses FL to ensure privacy while monitoring and forecasting the AQI in great detail. Every day, a city calculates and stores the AQI value. They can forecast the AQI index for that city for the next 'n' days based on the collected data. The FL idea is used to install the whole suggested system in a decentralized network. The suggested CNN-LSTM model predicts future AQI index with relatively low error, which cannot be conducted by the current single model (aggregated with all UAVs' combined weights in the swarm). The suggested CNN-LSTM model is compared against the other five models using different error measures. The outcome demonstrates that the suggested method, which combines FL with deep learning, is more accurate and one of the pioneering attempts in forecasting the air quality of a specific location. Moreover, using UAVs liked [47; 48], but [PERSON], et al. [49] suggests a novel framework for fine-grained 3D air quality monitoring and forecasting based on FL for aerial-ground air quality sensing. This system specifically uses a lightweight Dense-MobileNet model for airborne data to perform energy-efficient end-to-end learning from haze characteristics of hazy photos captured by UAVs for forecasting AQI scale distribution. Additionally, the FL Framework not only enlarges the extent of UAV swarms' monitoring but also enables many organizations or institutions to cooperatively build a well-trained global model to monitor AQI without sacrificing privacy. They suggest a Graph Convolutional Neural Network-based Long Short-Term Memory (GC-LSTM) model for ground sensing systems to accomplish precise, immediate, and future AQI inference. The aerial-ground sensing system can infer the AQI accurately thanks to the GC-LSTM model, which makes use of the topological structure of the ground monitoring station to capture the spatiotemporal correlation of historical observation data.