FedCert: Federated Accuracy Certification

Federated Learning (FL) has emerged as a powerful paradigm for training machine learning models in a decentralized manner, preserving data privacy by keeping local data on clients. However, evaluating the robustness of these models against data perturbations on clients remains a significant challenge. Previous studies have assessed the effectiveness of models in centralized training based on certified accuracy, which guarantees that a certain percentage of the model's predictions will remain correct even if the input data is perturbed. However, the challenge of extending these evaluations to FL remains unresolved due to the unknown client's local data. To tackle this challenge, this study proposed a method named FedCert to take the first step toward evaluating the robustness of FL systems. The proposed method is designed to approximate the certified accuracy of a global model based on the certified accuracy and class distribution of each client. Additionally, considering the Non-Independent and Identically Distributed (Non-IID) nature of data in real-world scenarios, we introduce the client grouping algorithm to ensure reliable certified accuracy during the aggregation step of the approximation algorithm. Through theoretical analysis, we demonstrate the effectiveness of FedCert in assessing the robustness and reliability of FL systems. Moreover, experimental results on the CIFAR-10 and CIFAR-100 datasets under various scenarios show that FedCert consistently reduces the estimation error compared to baseline methods. This study offers a solution for evaluating the robustness of FL systems and lays the groundwork for future research to enhance the dependability of decentralized learning. The source code is available at https://github.com/thanhhff/FedCert/.