Uncertainty-Aware Multidimensional Auctions for Social Welfare Optimization in Federated Learning

A federated learning framework enables multiple clients to jointly train models locally without uploading their private data, effectively protecting the clients’ data privacy. However, existing federated learning auction mechanisms have not considered heterogeneity in client training time, making it difficult for the server to aggregate client models effectively within a constrained time. Moreover, continuously selecting specific clients in each round can lead to overfitting. This article proposes an Uncertainty-aware Auction Mechanism (UAMARD) based on Age of Update (AoU), Reputation, and Data Quantity, which considers training time and provides guidance on the number of data points to participate in training for selected clients. Firstly, we model a reverse auction system that considers the uncertainty of training time to promote client participation. We introduce AoU to quantify the time interval required for the server to receive the latest updates from the client to avoid overfitting. Then, we prove that solving the problem of maximizing social welfare is NP-hard. Subsequently, we introduce a dynamic programming algorithm (VCG RA) to solve the problem of maximizing social welfare. To further reduce time complexity, we propose our UAMARD method, which achieves a near-optimal level of social welfare while ensuring minimal time complexity. Ultimately, simulation experiments confirmed the efficacy of UAMARD and VCG RA. When benchmarked against other mechanisms, UAMARD and VCG RA demonstrated superior performance with quicker convergence and higher accuracy in testing the MNIST and CIFAR-10 datasets.