Leveraging distributed computing resources and decentralized data iscrucial, ifnot necessary,for large-scale machine learning applications.

We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using M workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in M if given M rounds of synchronization, whereas FedAc only requires M^ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.

Summary and Contributions: The paper proposes a new version of Local-SGD/Federated Averaging algorithm -- Federated Accelerated SGD (FedAc). In particular, the algorithm solves a smooth convex expectation minimization problem in a distributed/federated fashion: M workers in parallel can access the stochastic gradients of the objective function and periodically communicate with a parameter-server. FedAc is a combination of AC-SA method from (Ghadimi and Lan, 2012) and Federated Averaging. Authors propose a first analysis of this method for generally strongly convex functions (in the convex case this method was analyzed in (Woodworth et al., 2020), but only for quadratic objectives) under the assumption that the variance of the stochastic gradients is uniformly bounded. The derived bounds outperform the state-of-the-art result for federated methods in this setting, and these rates are close to the accelerated ones. Moreover, authors show how their bounds improve under the additional assumption that the Hessian is Lipschitz continuous, and the 4-th central moment of the stochastic gradient is bounded and also extended known results for Local-SGD (FedAvg) to this case.

We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using M workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in M if given M rounds of synchronization, whereas FedAc only requires M ⅓ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.

Clustered federated learning (CFL) is proposed to mitigate the performance deterioration stemming from data heterogeneity in federated learning (FL) by grouping similar clients for cluster-wise model training. However, current CFL methods struggle due to inadequate integration of global and intra-cluster knowledge and the absence of an efficient online model similarity metric, while treating the cluster count as a fixed hyperparameter limits flexibility and robustness. In this paper, we propose an adaptive CFL framework, named FedAC, which (1) efficiently integrates global knowledge into intra-cluster learning by decoupling neural networks and utilizing distinct aggregation methods for each submodule, significantly enhancing performance; (2) includes a costeffective online model similarity metric based on dimensionality reduction; (3) incorporates a cluster number fine-tuning module for improved adaptability and scalability in complex, heterogeneous environments. Extensive experiments show that FedAC achieves superior empirical performance, increasing the test accuracy by around 1.82% and 12.67% on CIFAR-10 and CIFAR-100 datasets, respectively, under different non-IID settings compared to SOTA methods.

Stochastic optimization methods that leverage parallelism have proven immensely useful in modern optimization problems. Recent advances in machine learning have highlighted their importance as these techniques now rely on millions of parameters and increasingly large training sets. While there are many possible ways of parallelizing optimization algorithms, we consider the intermittent communication setting (Zinkevich et al., 2010; Cotter et al., 2011; Dekel et al., 2012; Shamir et al., 2014; Woodworth et al., 2018, 2021), where M parallel machines work together to optimize an objective during R rounds of communication, and where during each round each machine may perform some basic operation (e.g., access the objective by invoking some oracle) K times, and then communicate with all other machines. An important example of this setting is when this basic operation gives independent, unbiased stochastic estimates of the gradient, in which case this setting includes algorithms like Local SGD (Zinkevich et al., 2010; Coppola, 2015; Zhou and Cong, 2018; Stich, 2019; Woodworth et al., 2020a), Minibatch SGD (Dekel et al., 2012), Minibatch AC-SA (Ghadimi and Lan, 2012), and many others. We are motivated by the observation of Woodworth et al. (2020a) that for quadratic objectives, first-order methods such as one-shot averaging (Zinkevich et al., 2010; Zhang et al., 2013)--a special case of Local SGD with a single round of communication--can optimize the objective to a very high degree of accuracy. This prompts trying to reduce the task of optimizing general convex objectives to a short sequence of quadratic problems. Indeed, this is precisely the idea behind many second-order algorithms including Newton's method

We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a principled acceleration of Federated Averaging (FedAvg, also known as Local SGD) for distributed optimization. FedAc is the first provable acceleration of FedAvg that improves convergence speed and communication efficiency on various types of convex functions. For example, for strongly convex and smooth functions, when using $M$ workers, the previous state-of-the-art FedAvg analysis can achieve a linear speedup in $M$ if given $M$ rounds of synchronization, whereas FedAc only requires $M^{\frac{1}{3}}$ rounds. Moreover, we prove stronger guarantees for FedAc when the objectives are third-order smooth. Our technique is based on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability.