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Register a new userAchieving Statistical Optimality of Federated Learning: Beyond Stationary Points
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Federated Learning (FL) is a promising framework that has great potentials in privacy preservation and in lowering the computation load at the cloud. FedAvg and FedProx are two widely adopted algorithms. However, recent work raised concerns on these two methods: (1) their fixed points do not correspond to the stationary points of the original optimization problem, and (2) the common model found might not generalize well locally. In this paper, we alleviate these concerns. Towards this, we adopt the statistical learning perspective yet allow the distributions to be heterogeneous and the local data to be unbalanced. We show, in the general kernel regression setting, that both FedAvg and FedProx converge to the minimax-optimal error rates. Moreover, when the kernel function has a finite rank, the convergence is exponentially fast. Our results further analytically quantify the impact of the model heterogeneity and characterize the federation gain - the reduction of the estimation error for a worker to join the federated learning compared to the best local estimator. To the best of our knowledge, we are the first to show the achievability of minimax error rates under FedAvg and FedProx, and the first to characterize the gains in joining FL. Numerical experiments further corroborate our theoretical findings on the statistical optimality of FedAvg and FedProx and the federation gains.
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We propose a federated learning framework to handle heterogeneous client devices which do not conform to the population data distribution. The approach hinges upon a parameterized superquantile-based objective, where the parameter ranges over levels of conformity. We present an optimization algorithm and establish its convergence to a stationary point. We show how to practically implement it using secure aggregation by interleaving iterations of the usual federated averaging method with device filtering. We conclude with numerical experiments on neural networks as well as linear models on tasks from computer vision and natural language processing.
In this paper, we propose texttt{FedGLOMO}, the first (first-order) FL algorithm that achieves the optimal iteration complexity (i.e matching the known lower bound) on smooth non-convex objectives -- without using clients full gradient in each round. Our key algorithmic idea that enables attaining this optimal complexity is applying judicious momentum terms that promote variance reduction in both the local updates at the clients, and the global update at the server. Our algorithm is also provably optimal even with compressed communication between the clients and the server, which is an important consideration in the practical deployment of FL algorithms. Our experiments illustrate the intrinsic variance reduction effect of texttt{FedGLOMO} which implicitly suppresses client-drift in heterogeneous data distribution settings and promotes communication-efficiency. As a prequel to texttt{FedGLOMO}, we propose texttt{FedLOMO} which applies momentum only in the local client updates. We establish that texttt{FedLOMO} enjoys improved convergence rates under common non-convex settings compared to prior work, and with fewer assumptions.
Communication efficiency and robustness are two major issues in modern distributed learning framework. This is due to the practical situations where some computing nodes may have limited communication power or may behave adversarial behaviors. To address the two issues simultaneously, this paper develops two communication-efficient and robust distributed learning algorithms for convex problems. Our motivation is based on surrogate likelihood framework and the median and trimmed mean operations. Particularly, the proposed algorithms are provably robust against Byzantine failures, and also achieve optimal statistical rates for strong convex losses and convex (non-smooth) penalties. For typical statistical models such as generalized linear models, our results show that statistical errors dominate optimization errors in finite iterations. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.
Federated learning (FL) is a distributed machine learning architecture that leverages a large number of workers to jointly learn a model with decentralized data. FL has received increasing attention in recent years thanks to its data privacy protection, communication efficiency and a linear speedup for convergence in training (i.e., convergence performance increases linearly with respect to the number of workers). However, existing studies on linear speedup for convergence are only limited to the assumptions of i.i.d. datasets across workers and/or full worker participation, both of which rarely hold in practice. So far, it remains an open question whether or not the linear speedup for convergence is achievable under non-i.i.d. datasets with partial worker participation in FL. In this paper, we show that the answer is affirmative. Specifically, we show that the federated averaging (FedAvg) algorithm (with two-sided learning rates) on non-i.i.d. datasets in non-convex settings achieves a convergence rate $mathcal{O}(frac{1}{sqrt{mKT}} + frac{1}{T})$ for full worker participation and a convergence rate $mathcal{O}(frac{sqrt{K}}{sqrt{nT}} + frac{1}{T})$ for partial worker participation, where $K$ is the number of local steps, $T$ is the number of total communication rounds, $m$ is the total worker number and $n$ is the worker number in one communication round if for partial worker participation. Our results also reveal that the local steps in FL could help the convergence and show that the maximum number of local steps can be improved to $T/m$ in full worker participation. We conduct extensive experiments on MNIST and CIFAR-10 to verify our theoretical results.
Federated learning (FL) is a prevailing distributed learning paradigm, where a large number of workers jointly learn a model without sharing their training data. However, high communication costs could arise in FL due to large-scale (deep) learning models and bandwidth-constrained connections. In this paper, we introduce a communication-efficient algorithmic framework called CFedAvg for FL with non-i.i.d. datasets, which works with general (biased or unbiased) SNR-constrained compressors. We analyze the convergence rate of CFedAvg for non-convex functions with constant and decaying learning rates. The CFedAvg algorithm can achieve an $mathcal{O}(1 / sqrt{mKT} + 1 / T)$ convergence rate with a constant learning rate, implying a linear speedup for convergence as the number of workers increases, where $K$ is the number of local steps, $T$ is the number of total communication rounds, and $m$ is the total worker number. This matches the convergence rate of distributed/federated learning without compression, thus achieving high communication efficiency while not sacrificing learning accuracy in FL. Furthermore, we extend CFedAvg to cases with heterogeneous local steps, which allows different workers to perform a different number of local steps to better adapt to their own circumstances. The interesting observation in general is that the noise/variance introduced by compressors does not affect the overall convergence rate order for non-i.i.d. FL. We verify the effectiveness of our CFedAvg algorithm on three datasets with two gradient compression schemes of different compression ratios.
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