The minimax problems arise throughout machine learning applications, ranging from adversarial training and policy evaluation in reinforcement learning to AUROC maximization. To address the large-scale distributed data challenges across multiple clients with communication-efficient distributed training, federated learning (FL) is gaining popularity. Many optimization algorithms for minimax problems have been developed in the centralized setting (i.e., single-machine). Nonetheless, the algorithm for minimax problems under FL is still underexplored. In this paper, we study a class of federated nonconvex minimax optimization problems. We propose FL algorithms (FedSGDA+ and FedSGDA-M) and reduce existing complexity results for the most common minimax problems. For nonconvex-concave problems, we propose FedSGDA+ and reduce the communication complexity to O(ε 6). Under nonconvex-strongly-concave and nonconvex-PL minimax settings, we prove that FedSGDA-M has the best-known sample complexity of O(κ3N 1ε 3) and the best-known communication complexity of O(κ2ε 2). FedSGDA-M is the first algorithm to match the best sample complexity O(ε 3) achieved by the single-machine method under the nonconvex-strongly-concave setting.

Federated learning has attracted increasing attention due to the promise of balancing privacy and large-scale learning; numerous approaches have been proposed. However, most existing approaches focus on problems with balanced data, and prediction performance is far from satisfactory for many real-world applications where the number of samples in different classes is highly imbalanced. To address this challenging problem, we developed a novel federated learning method for imbalanced data by directly optimizing the area under curve (AUC) score. In particular, we formulate the AUC maximization problem as a federated compositional minimax optimization problem, develop a local stochastic compositional gradient descent ascent with momentum algorithm, and provide bounds on the computational and communication complexities of our algorithm. To the best of our knowledge, this is the first work to achieve such favorable theoretical results. Finally, extensive experimental results confirm the efficacy of our method.

Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the number of local updates, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on certain stochastic momentum estimator, the algorithm requires O( 3/2) samples and O( 1) communication rounds to compute an -stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such near-optimal sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between the number of local updates and the minibatch sizes, on which the above sample and communication complexities can be maintained. Finally, we show that for the classical FedAvg (a.k.a. Local SGD, which is a momentum-less special case of the STEM), a similar trade-off curve exists, albeit with worse sample and communication complexities. Our insights on this trade-off provides guidelines for choosing the four important design elements for FL algorithms, the number of local updates, WNs' and server's update directions, and minibatch sizes to achieve the best performance.

Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the number of local updates, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on certain stochastic momentum estimator, the algorithm requires O( 3/2) samples and O( 1) communication rounds to compute an -stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such near-optimal sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between the number of local updates and the minibatch sizes, on which the above sample and communication complexities can be maintained. Finally, we show that for the classical FedAvg (a.k.a. Local SGD, which is a momentum-less special case of the STEM), a similar trade-off curve exists, albeit with worse sample and communication complexities. Our insights on this trade-off provides guidelines for choosing the four important design elements for FL algorithms, the number of local updates, WNs' and server's update directions, and minibatch sizes to achieve the best performance.

Decentralized optimization are playing an important role in applications such as training large machine learning models, among others. Despite its superior practical performance, there has been some lack of fundamental understanding about its theoretical properties. In this work, we address the following open research question: To train an overparameterized model over a set of distributed nodes, what is the minimum communication overhead (in terms of the bits got exchanged) that the system needs to sustain, while still achieving (near) zero training loss? We show that for a class of overparameterized models where the number of parameters D is much larger than the total data samples N, the best possible communication complexity is (N), which is independent of the problem dimension D. Further, for a few specific overparameterized models (i.e., the linear regression, and certain multi-layer neural network with one wide layer), we develop a set of algorithms which uses certain linear compression followed by adaptive quantization, and show that they achieve dimension independent, near-optimal communication complexity. To our knowledge, this is the first time that dimension independent communication complexity has been shown for distributed optimization.