# An Improved Federated Learning-Assisted Data Aggregation Scheme for Smart Grids
## 4 Preliminaries
### Federated Learning  
In federated learning, multiple participants can collaboratively train a model without the need to centralize their original datasets. Instead, each participant retains their own data and conducts model training locally. By employing techniques such as encryption and secure computation, participants can aggregate the model's update information to achieve global performance improvement while preserving the privacy of individual data [23]. Federated learning enables the sharing of knowledge among multiple organizations or individuals, promoting the development and application of machine learning under the premise of sensitive data protection.  
There are two primary aspects of privacy in the context of learning: the privacy during the learning process [24], and the privacy of the learning outcome [25]. Privacy in the learning process refers to the process in which participants and the server transmit data between each other, and one of the participants infers the private data of the other participants from the data transmitted by the server. The privacy of the learning outcome involves the disclosure of intermediate data transmitted by participants and the server or the disclosure of the model (M) that the server ultimately obtains.  
Privacy in the learning process: In an FL environment, participant \(P_{i}\) ought to transmit the parameters of the local learning model \(x_{i}\) to the server, and if an attacker obtains \(x_{i}\), it is possible to infer \(P_{i}\)'s private data \(D_{i}\). Therefore, the risk of inferring \(x_{i}\) must be considered in a privacy-protected federated learning system.  
To address this potential risk, secure multi-party computation (SMC) is a widely adopted approach. In SMC, the security model inherently involves multiple participants and provides robust security proof within a well-defined simulation framework. This framework ensures \"absolute zero knowledge\", meaning that each participant remains completely unaware of any information other than their own inputs and outputs. Zero-knowledge is highly desirable due to its enhanced data privacy and security features. However, achieving such properties often requires the implementation of more complex computational protocols, which might not always be practical. Under certain circumstances, accepting partial knowledge disclosure might be considered acceptable, as long as adequate security assurances are provided. While SMC effectively mitigates risks during the learning process, it is important to recognize that federated learning systems relying solely on SMC may still be susceptible to learning outcome inferences. Consequently, privacy-protecting FL systems must also account for potential inferences related to the learning outcomes. This entails incorporating additional measures or protocols to prevent unauthorized access or inference of sensitive information regarding the learning process results.  
Privacy of learning outcomes: Learning outcomes encompass the intermediate outcomes attained throughout the federated learning process as well as the ultimate learning model. Several studies have demonstrated that an attacker can deduce information about the training data [25]. Consequently, in a federated learning environment, the inference made regarding the learning outcome must adhere to the principle that the owner \(\mathcal{U}_{i}\) of the data \(D_{i}\) is the only party capable of inferring any outcome related to \(D_{i}\).  
The differential privacy (DP) framework is commonly employed to address privacy concerns pertaining to output results [26]. By introducing noise to the data through differential privacy, applying techniques like \(k\)-anonymity or diversification, or by utilizing inductive methods to obfuscate sensitive attributes, the data become indistinguishable, safeguarding user privacy. Nonetheless, these approaches often necessitate the transfer of data to external entities, resulting in a trade-off between accuracy and privacy.