Honglin Yuan

Honglin Yuan

Federated Learning (FL), a distributed learning paradigm that scales on-device learning collaboratively, has emerged as a promising approach for decentralized AI applications. Local optimization methods such as Federated Averaging (FedAvg) are the most prominent methods for FL applications. Despite their simplicity and popularity, the theoretical understanding of local optimization methods is far from clear. This dissertation aims to advance the theoretical foundation of local methods in the following three directions. First, we establish sharp bounds for FedAvg, the most popular algorithm in Federated Learning. We demonstrate how FedAvg may suffer from a notion we call iterate bias, and how an additional third-order smoothness assumption may mitigate this effect and lead to better convergence rates. We explain this phenomenon from a Stochastic Differential Equation (SDE) perspective. Second, we propose Federated Accelerated Stochastic Gradient Descent (FedAc), the first principled acceleration of FedAvg, which provably improves the convergence rate and communication efficiency. Our technique uses on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability. Third, we study the Federated Composite Optimization problem, which extends the classic smooth setting by incorporating a shared non-smooth regularizer. We show that direct extensions of FedAvg may suffer from the "curse of primal averaging," resulting in slow convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging, which overcomes the curse of primal averaging by employing a novel inter-client dual averaging procedure.

Margalit Glasgow, Honglin Yuan, Tengyu Ma

Federated Averaging (FedAvg), also known as Local SGD, is one of the most popular algorithms in Federated Learning (FL). Despite its simplicity and popularity, the convergence rate of FedAvg has thus far been undetermined. Even under the simplest assumptions (convex, smooth, homogeneous, and bounded covariance), the best-known upper and lower bounds do not match, and it is not clear whether the existing analysis captures the capacity of the algorithm. In this work, we first resolve this question by providing a lower bound for FedAvg that matches the existing upper bound, which shows the existing FedAvg upper bound analysis is not improvable. Additionally, we establish a lower bound in a heterogeneous setting that nearly matches the existing upper bound. While our lower bounds show the limitations of FedAvg, under an additional assumption of third-order smoothness, we prove more optimistic state-of-the-art convergence results in both convex and non-convex settings. Our analysis stems from a notion we call iterate bias, which is defined by the deviation of the expectation of the SGD trajectory from the noiseless gradient descent trajectory with the same initialization. We prove novel sharp bounds on this quantity, and show intuitively how to analyze this quantity from a Stochastic Differential Equation (SDE) perspective.

Jonathan Kelner, Annie Marsden, Vatsal Sharan et al.

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly decomposable as the sum of $m$ unknown non-interacting smooth, strongly convex functions and provide a method which solves this problem with a number of gradient evaluations that scales (up to logarithmic factors) as the product of the square-root of the condition numbers of the components. This complexity bound (which we prove is nearly optimal) can improve almost exponentially on that of accelerated gradient methods, which grow as the square root of the condition number of $f$. Additionally, we provide efficient methods for solving stochastic, quadratic variants of this multiscale optimization problem. Rather than learn the decomposition of $f$ (which would be prohibitively expensive), our methods apply a clean recursive "Big-Step-Little-Step" interleaving of standard methods. The resulting algorithms use $\tilde{\mathcal{O}}(d m)$ space, are numerically stable, and open the door to a more fine-grained understanding of the complexity of convex optimization beyond condition number.

Honglin Yuan, Warren Morningstar, Lin Ning et al.

Federated learning data is drawn from a distribution of distributions: clients are drawn from a meta-distribution, and their data are drawn from local data distributions. Thus generalization studies in federated learning should separate performance gaps from unseen client data (out-of-sample gap) from performance gaps from unseen client distributions (participation gap). In this work, we propose a framework for disentangling these performance gaps. Using this framework, we observe and explain differences in behavior across natural and synthetic federated datasets, indicating that dataset synthesis strategy can be important for realistic simulations of generalization in federated learning. We propose a semantic synthesis strategy that enables realistic simulation without naturally-partitioned data. Informed by our findings, we call out community suggestions for future federated learning works.

Jianyu Wang, Zachary Charles, Zheng Xu et al.

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.

Honglin Yuan, Manzil Zaheer, Sashank Reddi

Federated Learning (FL) is a distributed learning paradigm that scales on-device learning collaboratively and privately. Standard FL algorithms such as FedAvg are primarily geared towards smooth unconstrained settings. In this paper, we study the Federated Composite Optimization (FCO) problem, in which the loss function contains a non-smooth regularizer. Such problems arise naturally in FL applications that involve sparsity, low-rank, monotonicity, or more general constraints. We first show that straightforward extensions of primal algorithms such as FedAvg are not well-suited for FCO since they suffer from the "curse of primal averaging," resulting in poor convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging (FedDualAvg), which by employing a novel server dual averaging procedure circumvents the curse of primal averaging. Our theoretical analysis and empirical experiments demonstrate that FedDualAvg outperforms the other baselines.

Honglin Yuan, Tengyu Ma

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.