Title: Federated Learning on Adaptively Weighted Nodes by Bilevel Optimization. Abstract: We propose a federated learning method with weighted nodes in which the weights can be modified to optimize the model’s performance on a separate validation set. The problem is formulated as a bilevel optimization problem where the inner problem is a federated learning problem with weighted nodes and the outer problem focuses on optimizing the weights based on the validation performance of the model returned from the inner problem. A communication-efficient federated optimization algorithm is designed to solve this bilevel optimization problem. We analyze the generalization performance of the output model and identify the scenarios when our method is in theory superior to training a model locally and superior to federated learning with static and evenly distributed weights. 