Optimal Contract Design for Efficient Federated Learning With Multi-Dimensional Private Information

As an emerging machine learning technique, federated learning has received significant attention recently due to its promising performance in mitigating privacy risks and costs. While most of the existing work of federated learning focused on designing learning algorithm to improve training performance, the incentive issue for encouraging users' participation is still under-explored. This paper presents an analytical study on the server's optimal incentive mechanism design, in the presence of users' multi-dimensional private information (e.g., training cost and communication delay). Specifically, we consider a multi-dimensional contract-theoretic approach, with a key contribution of summarizing users' multi-dimensional private information into a one-dimensional criterion that allows a complete order of users. We further perform the analysis in three information scenarios to reveal the impact of information asymmetry levels on server's optimal strategy and minimum cost. We show that weakly incomplete information does not increase the server's cost (comparing with the complete information scenario) when training data is IID, but it in general does when data is non-IID. Furthermore, the optimal mechanism design under strongly incomplete information is much more challenging, and it is not always optimal for the server to incentivize the group of users with the lowest training cost and delay to participate.