Title: Anchor Sampling for Federated Learning with Partial Client Participation. Abstract: In federated learning, the support of partial client participation offers a flexible training strategy, but it deteriorates the model training efficiency. In this paper, we propose a framework FedAMD to improve the convergence property and maintain flexibility. The core idea is anchor sampling, which disjoints the partial participants into anchor and miner groups. Each client in the anchor group aims at the local bullseye with the gradient computation using a large batch. Guided by the bullseyes, clients in the miner group steer multiple near-optimal local updates using small batches and update the global model. With the joint efforts from both groups, FedAMD is able to accelerate the training process as well as improve the model performance. Measured by $\epsilon$-approximation and compared to the state-of-the-art first-order methods, FedAMD achieves the convergence by up to $O(1/\epsilon)$ fewer communication rounds under non-convex objectives. In specific, we achieve a linear convergence rate under PL conditions. Empirical studies on real-world datasets validate the effectiveness of FedAMD and demonstrate the superiority of our proposed algorithm: Not only does it considerably save computation and communication costs, but also the test accuracy significantly improves. 