An Incentive Mechanism for Cross-Silo Federated Learning: A Public Goods Perspective

In cross-silo federated learning (FL), organizations cooperatively train a global model with their local data. The organizations, however, may be heterogeneous in terms of their valuation on the precision of the trained global model and their training cost. Meanwhile, the computational and communication resources of the organizations are non-excludable public goods. That is, even if an organization does not perform any local training, other organizations cannot prevent that organization from using the outcome of their resources (i.e., the trained global model). To address the organization heterogeneity and the public goods feature, in this paper, we formulate a social welfare maximization problem and propose an incentive mechanism for cross-silo FL. With the proposed mechanism, organizations can achieve not only social welfare maximization but also individual rationality and budget balance. Moreover, we propose a distributed algorithm that enables organizations to maximize the social welfare without knowing the valuation and cost of each other. Our simulations with MNIST dataset show that the proposed algorithm converges faster than a benchmark method. Furthermore, when organizations have higher valuation on precision, the proposed mechanism and algorithm are more beneficial in the sense that the organizations can achieve higher social welfare through participating in cross-silo FL.

I. Introduction

Federated learning (FL) [1] is a decentralized machine learning approach. In FL, multiple clients cooperatively train a global model with their local data under the coordination of a central server. During the training phase, each client periodically downloads the global model from the central server, updates its local model by training the downloaded global model with its local data, and uploads the model updates to the central server for global model updating. Since each client does not need to transfer its local data to the central server, data privacy can be preserved. FL can be classified into two types [1]: cross-device FL and cross-silo FL. In cross-device FL, as shown in Fig. 1 (a), an organization (e.g., company, institution) acts as the central server. This organization is the owner of the global model. That is, it initiates the FL and owns the trained global model. The devices are the clients and perform local training. On the other hand, in cross-silo FL, as shown in Fig. 1 (b), a third party entity acts as the central server and is responsible for the coordination of training. A set of organizations act as the clients to perform local training. They are also the owners of the global model and can make use of the trained global model.