Title: Adaptive Client Sampling in Federated Learning via Online Learning with Bandit Feedback. Abstract: Due to the high cost of communication, federated learning (FL) systems need to sample a subset of clients that are involved in each round of training. As a result, client sampling plays an important role in FL systems as it affects the convergence rate of optimization algorithms used to train machine learning models. Despite its importance, there is limited work on how to sample clients effectively. In this paper, we cast client sampling as an online learning task with bandit feedback, which we solve with an online stochastic mirror descent (OSMD) algorithm designed to minimize the sampling variance. We then theoretically show how our sampling method can improve the convergence speed of optimization algorithms. To handle the tuning parameters in OSMD that depend on the unknown problem parameters, we use the online ensemble method and doubling trick. We prove a dynamic regret bound relative to any sampling sequence. The regret bound depends on the total variation of the comparator sequence, which naturally captures the intrinsic difficulty of the problem. To the best of our knowledge, these theoretical contributions are new and the proof technique is of independent interest. Through both synthetic and real data experiments, we illustrate advantages of the proposed client sampling algorithm over the widely used uniform sampling and existing online learning based sampling strategies. The proposed adaptive sampling procedure is applicable beyond the FL problem studied here and can be used to improve the performance of stochastic optimization procedures such as stochastic gradient descent and stochastic coordinate descent.