Simultaneous network gradient descent for decentralized federated learning with missing data

In this paper, we focus on decentralized federated learning with missing data. Decentralized learning based on fully observed data has drawn attention in the modern statistical learning. In practice, however, missing data are often encountered such that the existing methods cannot be applied. To address the missing data issue, a novel decentralized algorithm is proposed by using inverse probability weighting in conjunction with network gradient descent method to correct bias and improve estimation together. In order to reduce the computation cost and make the algorithm converge fast, updating the nuisance propensity parameter and target parameter simultaneously at each iteration is proposed. Theoretically, the convergence guarantees of our proposed algorithm are provided and the error bound of the proposed estimator is also studied. The finite-sample performance is investigated through simulations under both independent and identically distributed (i.i.d.) and non-i.i.d. cases. An application to Communities and Crime Data is also presented.