Federated Learning (FL) makes a large amount of edge computing devices (e.g., mobile phones) jointly learn a global model without data sharing. In FL, data are generated in a decentralized manner with high heterogeneity. This paper studies how to perform statistical estimation and inference in the federated setting. We analyze the so-called Local SGD, a multi-round estimation procedure that uses intermittent communication to improve communication efficiency. We first establish a {\it functional central limit theorem} that shows the averaged iterates of Local SGD weakly converge to a rescaled Brownian motion. We next provide two iterative inference methods: the {\it plug-in} and the {\it random scaling}. Random scaling constructs an asymptotically pivotal statistic for inference by using the information along the whole Local SGD path. Both the methods are communication efficient and applicable to online data. Our theoretical and empirical results show that Local SGD simultaneously achieves both statistical efficiency and communication efficiency.
Renmin University of China（中国人民大学）；Kyoto University（京都大学）
As massive data are produced from small gadgets, federated learning on mobile devices has become an emerging trend. In the federated setting, Stochastic Gradient Descent (SGD) has been widely used in federated learning for various machine learning models. To prevent privacy leakages from gradients that are calculated on users' sensitive data, local differential privacy (LDP) has been considered as a privacy guarantee in federated SGD recently. However, the existing solutions have a dimension dependency problem: the injected noise is substantially proportional to the dimension $d$. In this work…
University of Southern California（南加州大学）；Amazon Alexa AI（亚马逊 Alexa AI）
Local Stochastic Gradient Descent (SGD) with periodic model averaging (FedAvg) is a foundational algorithm in Federated Learning. The algorithm independently runs SGD on multiple workers and periodically averages the model across all the workers. When local SGD runs with many workers, however, the periodic averaging causes a significant model discrepancy across the workers making the global loss converge slowly. While recent advanced optimization methods tackle the issue focused on non-IID settings, there still exists the model discrepancy issue due to the underlying periodic model averaging. …
The Chinese University of Hong Kong（香港中文大学）；Huawei Technologies Co. Ltd（华为技术有限公司）
The high cost of communicating gradients is a major bottleneck for federated learning, as the bandwidth of the participating user devices is limited. Existing gradient compression algorithms are mainly designed for data centers with high-speed network and achieve $O(\sqrt{d} \log d)$ per-iteration communication cost at best, where $d$ is the size of the model. We propose hyper-sphere quantization (HSQ), a general framework that can be configured to achieve a continuum of trade-offs between communication efficiency and gradient accuracy. In particular, at the high compression ratio end, HSQ pro…
The Blavatnik School of Computer Science（布拉瓦尼克计算机科学学院）；Tel Aviv University（特拉维夫大学）
This work presents a new distributed Byzantine tolerant federated learning algorithm, HoldOut SGD, for Stochastic Gradient Descent (SGD) optimization. HoldOut SGD uses the well known machine learning technique of holdout estimation, in a distributed fashion, in order to select parameter updates that are likely to lead to models with low loss values. This makes it more effective at discarding Byzantine workers inputs than existing methods that eliminate outliers in the parameter-space of the learned model. HoldOut SGD first randomly selects a set of workers that use their private data in order …
Privacy regulation laws, such as GDPR, impose transparency and security as design pillars for data processing algorithms. In this context, federated learning is one of the most influential frameworks for privacy-preserving distributed machine learning, achieving astounding results in many natural language processing and computer vision tasks. Several federated learning frameworks employ differential privacy to prevent private data leakage to unauthorized parties and malicious attackers. Many studies, however, highlight the vulnerabilities of standard federated learning to poisoning and inferen…
NTT DATA Mathematical Systems Inc.（NTT数据数学系统公司）；The University of Tokyo（东京大学）；RIKEN（理化学研究所）
Recently, local SGD has got much attention and been extensively studied in the distributed learning community to overcome the communication bottleneck problem. However, the superiority of local SGD to minibatch SGD only holds in quite limited situations. In this paper, we study a new local algorithm called Bias-Variance Reduced Local SGD (BVR-L-SGD) for nonconvex distributed optimization. Algorithmically, our proposed bias and variance reduced local gradient estimator fully utilizes small second-order heterogeneity of local objectives and suggests randomly picking up one of the local models in…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学（KAUST））
In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic gradient. Our assumption is satisfied by a large number of specific variants of SGD in the literature, including SGD with arbitrary sampling, SGD with compressed gradients, and a wide variety of variance-reduced SGD methods such as SVRG and SAGA. We provide a single convergence analysis for all methods that satisfy the proposed unified assumption, thereby offering a…
School of Computer Science and Technology, Huazhong University of Science and Technology（华中科技大学计算机科学与技术学院）；Department of Computing, The Hong Kong Polytechnic University（香港理工大学计算学系）；College of Computer and Information, Hohai University（河海大学计算机与信息学院）；Department of Computer Science and Engineering, Nanjing University（南京大学计算机科学与技术系）
Federated Learning is a powerful machine learning paradigm to cooperatively train a global model with highly distributed data. A major bottleneck on the performance of distributed Stochastic Gradient Descent (SGD) algorithm for large-scale Federated Learning is the communication overhead on pushing local gradients and pulling global model. In this paper, to reduce the communication complexity of Federated Learning, a novel approach named Pulling Reduction with Local Compensation (PRLC) is proposed. Specifically, each training node intermittently pulls the global model from the server in SGD it…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；University of Helsinki（赫尔辛基大学）
We propose an algorithm for the adaptation of the learning rate for stochastic gradient descent (SGD) that avoids the need for validation set use. The idea for the adaptiveness comes from the technique of extrapolation: to get an estimate for the error against the gradient flow which underlies SGD, we compare the result obtained by one full step and two half-steps. The algorithm is applied in two separate frameworks: federated and differentially private learning. Using examples of deep neural networks we empirically show that the adaptive algorithm is competitive with manually tuned commonly u…
A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show that data heterogeneity can in fact be exploited to improve generalization performance through implicit regularization. One way to alleviate the effects of heterogeneity is to encourage the alignment of gradients across different clients throughout training. Our analysis reveals that this goal can be accomplished by utilizing the right optimization method that…
Decentralized stochastic gradient descent (SGD) is a driving engine for decentralized federated learning (DFL). The performance of decentralized SGD is jointly influenced by inter-node communications and local updates. In this paper, we propose a general DFL framework, which implements both multiple local updates and multiple inter-node communications periodically, to strike a balance between communication efficiency and model consensus. It can provide a general decentralized SGD analytical framework. We establish strong convergence guarantees for the proposed DFL algorithm without the assumpt…
SecureDrive-FL: Joint Differential Privacy and Gradient-Aware Selective Homomorphic Encryption for Federated Driver Monitoring
Institute of Industrial Automation and Software Engineering, University of Stuttgart（斯图加特大学工业自动化与软件工程研究所）；Eindhoven University of Technology (TU/e)（埃因霍温理工大学）
Federated learning (FL) has become a hot research area in enabling the collaborative training of machine learning models among multiple clients that hold sensitive local data. Nevertheless, unconstrained federated optimization has been studied mainly using stochastic gradient descent (SGD), which may converge slowly, and constrained federated optimization, which is more challenging, has not been investigated so far. This paper investigates sample-based and feature-based federated optimization, respectively, and considers both unconstrained and constrained nonconvex problems for each of them. F…
The University of British Columbia（不列颠哥伦比亚大学）；University of Minnesota（明尼苏达大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Shenzhen University（深圳大学）
This work investigates fault-resilient federated learning when the data samples are non-uniformly distributed across workers, and the number of faulty workers is unknown to the central server. In the presence of adversarially faulty workers who may strategically corrupt datasets, the local messages exchanged (e.g., local gradients and/or local model parameters) can be unreliable, and thus the vanilla stochastic gradient descent (SGD) algorithm is not guaranteed to converge. Recently developed algorithms improve upon vanilla SGD by providing robustness to faulty workers at the price of slowing …
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We propose a new optimization formulation for training federated learning models. The standard formulation has the form of an empirical risk minimization problem constructed to find a single global model trained from the private data stored across all participating devices. In contrast, our formulation seeks an explicit trade-off between this traditional global model and the local models, which can be learned by each device from its own private data without any communication. Further, we develop several efficient variants of SGD (with and without partial participation and with and without vari…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
In this work, we consider the optimization formulation of personalized federated learning recently introduced by Hanzely and Richtárik (2020) which was shown to give an alternative explanation to the workings of local {\tt SGD} methods. Our first contribution is establishing the first lower bounds for this formulation, for both the communication complexity and the local oracle complexity. Our second contribution is the design of several optimal methods matching these lower bounds in almost all regimes. These are the first provably optimal methods for personalized federated learning. Our optima…
Xidian University（西安电子科技大学）；JD Tech（京东科技）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；JD Finance America Corporation（京东金融美国公司）；Simon Fraser University（西蒙弗雷泽大学）；University of Pittsburgh（匹兹堡大学）
Vertical federated learning (VFL) is an effective paradigm of training the emerging cross-organizational (e.g., different corporations, companies and organizations) collaborative learning with privacy preserving. Stochastic gradient descent (SGD) methods are the popular choices for training VFL models because of the low per-iteration computation. However, existing SGD-based VFL algorithms are communication-expensive due to a large number of communication rounds. Meanwhile, most existing VFL algorithms use synchronous computation which seriously hamper the computation resource utilization in re…
Federated Learning (FL) is a recent development in distributed machine learning that collaboratively trains models without training data leaving client devices, preserving data privacy. In real-world FL, the training set is distributed over clients in a highly non-Independent and Identically Distributed (non-IID) fashion, harming model convergence speed and final performance. To address this challenge, we propose a novel, generalised approach for incorporating adaptive optimisation into FL with the Federated Global Biased Optimiser (FedGBO) algorithm. FedGBO accelerates FL by employing a set o…
In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non i.i.d. data samples). In this paper, we generalize the local stochastic and full gradient descent with periodic averaging-- originally designed for homogeneous distributed optimization, to solve nonconvex optimization problems in federated learning. Although scant research is available on the effectiveness of local SGD in reducing the number of communication ro…
Federated Averaging (FedAvg, also known as Local-SGD) (McMahan et al., 2017) is a classical federated learning algorithm in which clients run multiple local SGD steps before communicating their update to an orchestrating server. We propose a new federated learning algorithm, FedPAGE, able to further reduce the communication complexity by utilizing the recent optimal PAGE method (Li et al., 2021) instead of plain SGD in FedAvg. We show that FedPAGE uses much fewer communication rounds than previous local methods for both federated convex and nonconvex optimization. Concretely, 1) in the convex …
We study stochastic gradient descent (SGD) with local iterations in the presence of malicious/Byzantine clients, motivated by the federated learning. The clients, instead of communicating with the central server in every iteration, maintain their local models, which they update by taking several SGD iterations based on their own datasets and then communicate the net update with the server, thereby achieving communication-efficiency. Furthermore, only a subset of clients communicate with the server, and this subset may be different at different synchronization times. The Byzantine clients may c…
We consider learning a multi-class classification model in the federated setting, where each user has access to the positive data associated with only a single class. As a result, during each federated learning round, the users need to locally update the classifier without having access to the features and the model parameters for the negative classes. Thus, naively employing conventional decentralized learning such as the distributed SGD or Federated Averaging may lead to trivial or extremely poor classifiers. In particular, for the embedding based classifiers, all the class embeddings might …
Federated learning (FL) has emerged as a privacy solution for collaborative distributed learning where clients train AI models directly on their devices instead of sharing their data with a centralized (potentially adversarial) server. Although FL preserves local data privacy to some extent, it has been shown that information about clients' data can still be inferred from model updates. In recent years, various privacy-preserving schemes have been developed to address this privacy leakage. However, they often provide privacy at the expense of model performance or system efficiency, and balanci…
Acceleration of stochastic gradient descent with momentum by averaging: finite-sample rates and asymptotic normality
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Daniels School of Business, Purdue University（普渡大学丹尼尔斯商学院）；Stern School of Business, New York University（纽约大学斯特恩商学院）
Statistical Inference for Differentially Private Stochastic Gradient Descent
Center for Data Science, Zhejiang University（浙江大学数据科学中心）；Department of Statistics, Rutgers University（罗格斯大学统计系）；Faculty of Business and Economics, The University of Hong Kong（香港大学商学院）
Communication efficiency is crucial for federated learning (FL). Conducting local training steps in clients to reduce the communication frequency between clients and the server is a common method to address this issue. However, this strategy leads to the client drift problem due to \textit{non-i.i.d.} data distributions in different clients which severely deteriorates the performance. In this work, we propose a new method to improve the training performance in cross-silo FL via maintaining double momentum buffers. In our algorithm, one momentum buffer is used to track the server model updating…
Koç University（科奇大学）；Imperial College London（伦敦帝国理工学院）
Federated learning (FL) has become de facto framework for collaborative learning among edge devices with privacy concern. The core of the FL strategy is the use of stochastic gradient descent (SGD) in a distributed manner. Large scale implementation of FL brings new challenges, such as the incorporation of acceleration techniques designed for SGD into the distributed setting, and mitigation of the drift problem due to non-homogeneous distribution of local datasets. These two problems have been separately studied in the literature; whereas, in this paper, we show that it is possible to address …
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；IBM T.J. Watson Research Center, Yorktown Heights（IBM T.J. Watson 研究中心，约克镇高地）
We present a novel method for frequentist statistical inference in $M$-estimation problems, based on stochastic gradient descent (SGD) with a fixed step size: we demonstrate that the average of such SGD sequences can be used for statistical inference, after proper scaling. An intuitive analysis using the Ornstein-Uhlenbeck process suggests that such averages are asymptotically normal. From a practical perspective, our SGD-based inference procedure is a first order method, and is well-suited for large scale problems. To show its merits, we apply it to both synthetic and real datasets, and demon…
Federated Learning is a distributed machine learning approach which enables model training without data sharing. In this paper, we propose a new federated learning algorithm, Federated Averaging with Client-level Momentum (FedCM), to tackle problems of partial participation and client heterogeneity in real-world federated learning applications. FedCM aggregates global gradient information in previous communication rounds and modifies client gradient descent with a momentum-like term, which can effectively correct the bias and improve the stability of local SGD. We provide theoretical analysis …
Kakao Entertainment Corp.（Kakao娱乐公司）；Seoul National University（首尔大学）
The implicit stochastic gradient descent (ISGD), a proximal version of SGD, is gaining interest in the literature due to its stability over (explicit) SGD. In this paper, we conduct an in-depth analysis of the two modes of ISGD for smooth convex functions, namely proximal Robbins-Monro (proxRM) and proximal Poylak-Ruppert (proxPR) procedures, for their use in statistical inference on model parameters. Specifically, we derive non-asymptotic point estimation error bounds of both proxRM and proxPR iterates and their limiting distributions, and propose on-line estimators of their asymptotic covari…
National Tsing Hua University（国立清华大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）
Federated learning (FL) is a new paradigm that enables many clients to jointly train a machine learning (ML) model under the orchestration of a parameter server while keeping the local data not being exposed to any third party. However, the training of FL is an interactive process between local clients and the parameter server. Such process would cause privacy leakage since adversaries may retrieve sensitive information by analyzing the overheard messages. In this paper, we propose a new federated stochastic primal-dual algorithm with differential privacy (FedSPD-DP). Compared to the existing …
On the Limits of Momentum in Decentralized and Federated Optimization
Department of Computer and Control Engineering, Polytechnic of Turin（计算机与控制工程系，都灵理工学院）；Thomas Lord Department of Computer Science, USC Viterbi School of Engineering（托马斯·劳德计算机科学系，USC维特里商学院）
JD Finance America Corporation（京东金融美国公司）；Department of Electrical & Computer Engineering, University of Pittsburgh（匹兹堡大学电气与计算机工程系）；University of Pittsburgh（匹兹堡大学）
The privacy-preserving federated learning for vertically partitioned data has shown promising results as the solution of the emerging multi-party joint modeling application, in which the data holders (such as government branches, private finance and e-business companies) collaborate throughout the learning process rather than relying on a trusted third party to hold data. However, existing federated learning algorithms for vertically partitioned data are limited to synchronous computation. To improve the efficiency when the unbalanced computation/communication resources are common among the pa…
Ant Group（蚂蚁集团）；Shanghai Jiao Tong University（上海交通大学）；University of Minnesota（明尼苏达大学）
The vanilla Differentially-Private Stochastic Gradient Descent (DP-SGD), including DP-Adam and other variants, ensures the privacy of training data by uniformly distributing privacy costs across training steps. The equivalent privacy costs controlled by maintaining the same gradient clipping thresholds and noise powers in each step result in unstable updates and a lower model accuracy when compared to the non-DP counterpart. In this paper, we propose the dynamic DP-SGD (along with dynamic DP-Adam, and others) to reduce the performance loss gap while maintaining privacy by dynamically adjusting…
As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery problems in the FL setting, whose loss function consists of a data-dependent smooth loss and a non-smooth regularizer. Examples include sparse linear regression using Lasso, low-rank matrix recovery using nuclear norm regularization, etc. In the existing literature, federated composite optimization algorithms are designed only from an optimization perspective w…
Federated learning (FL) allows to train a massive amount of data privately due to its decentralized structure. Stochastic gradient descent (SGD) is commonly used for FL due to its good empirical performance, but sensitive user information can still be inferred from weight updates shared during FL iterations. We consider Gaussian mechanisms to preserve local differential privacy (LDP) of user data in the FL model with SGD. The trade-offs between user privacy, global utility, and transmission rate are proved by defining appropriate metrics for FL with LDP. Compared to existing results, the query…
In recent years, distributed optimization is proven to be an effective approach to accelerate training of large scale machine learning models such as deep neural networks. With the increasing computation power of GPUs, the bottleneck of training speed in distributed training is gradually shifting from computation to communication. Meanwhile, in the hope of training machine learning models on mobile devices, a new distributed training paradigm called ``federated learning'' has become popular. The communication time in federated learning is especially important due to the low bandwidth of mobile…
The large communication cost for exchanging gradients between different nodes significantly limits the scalability of distributed training for large-scale learning models. Motivated by this observation, there has been significant recent interest in techniques that reduce the communication cost of distributed Stochastic Gradient Descent (SGD), with gradient sparsification techniques such as top-k and random-k shown to be particularly effective. The same observation has also motivated a separate line of work in distributed statistical estimation theory focusing on the impact of communication con…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Google Research（谷歌研究院）；Boston University（波士顿大学）
Motivated by recent applications requiring differential privacy over adaptive streams, we investigate the question of optimal instantiations of the matrix mechanism in this setting. We prove fundamental theoretical results on the applicability of matrix factorizations to adaptive streams, and provide a parameter-free fixed-point algorithm for computing optimal factorizations. We instantiate this framework with respect to concrete matrices which arise naturally in machine learning, and train user-level differentially private models with the resulting optimal mechanisms, yielding significant imp…
We consider training models with differential privacy (DP) using mini-batch gradients. The existing state-of-the-art, Differentially Private Stochastic Gradient Descent (DP-SGD), requires privacy amplification by sampling or shuffling to obtain the best privacy/accuracy/computation trade-offs. Unfortunately, the precise requirements on exact sampling and shuffling can be hard to obtain in important practical scenarios, particularly federated learning (FL). We design and analyze a DP variant of Follow-The-Regularized-Leader (DP-FTRL) that compares favorably (both theoretically and empirically) …
