The heart of Quantum Federated Learning (QFL) is associated with a distributed learning architecture across several local quantum devices and a more efficient training algorithm for the QFL is expected to minimize the communication overhead among different quantum participants. In this work, we put forth an efficient learning algorithm, namely federated quantum natural gradient descent (FQNGD), applied in a QFL framework which consists of the variational quantum circuit (VQC)-based quantum neural networks (QNN). The FQNGD algorithm admits much fewer training iterations for the QFL model to get converged and it can significantly reduce the total communication cost among local quantum devices. Compared with other federated learning algorithms, our experiments on a handwritten digit classification dataset corroborate the effectiveness of the FQNGD algorithm for the QFL in terms of a faster convergence rate on the training dataset and higher accuracy on the test one.
Fudan University（复旦大学）；Georgia Institute of Technology（佐治亚理工学院）；Northwestern Polytechnical University（西北工业大学）；Universidad San Pablo-CEU, CEU Universities（CEU大学圣巴勃罗-CEU大学）
Quantum federated learning (QFL) is a quantum extension of the classical federated learning model across multiple local quantum devices. An efficient optimization algorithm is always expected to minimize the communication overhead among different quantum participants. In this work, we propose an efficient optimization algorithm, namely federated quantum natural gradient descent (FQNGD), and further, apply it to a QFL framework that is composed of a variational quantum circuit (VQC)-based quantum neural networks (QNN). Compared with stochastic gradient descent methods like Adam and Adagrad, the…
Federated learning enables multiple, distributed participants (potentially on different clouds) to collaborate and train machine/deep learning models by sharing parameters/gradients. However, sharing gradients, instead of centralizing data, may not be as private as one would expect. Reverse engineering attacks on plaintext gradients have been demonstrated to be practically feasible. Existing solutions for differentially private federated learning, while promising, lead to less accurate models and require nontrivial hyperparameter tuning. In this paper, we examine the use of additive homomorphi…
Zhejiang University/University of Illinois at Urbana-Champaign Institute（浙江大学-伊利诺伊大学厄巴纳香槟校区联合学院）；Hong Kong Metropolitan University（香港都会大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Princeton University（普林斯顿大学）
Federated learning (FL) is an emerging machine learning method that can be applied in mobile edge systems, in which a server and a host of clients collaboratively train a statistical model utilizing the data and computation resources of the clients without directly exposing their privacy-sensitive data. We show that running stochastic gradient descent (SGD) in such a setting can be viewed as adding a momentum-like term to the global aggregation process. Based on this finding, we further analyze the convergence rate of a federated learning system by accounting for the effects of parameter stale…
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…
University of Science and Technology of China（中国科学技术大学）；University of Warwick（华威大学）
Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this paper, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence pr…
This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by one of the agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is show…
Chongqing University of Posts and Telecommunications（重庆邮电大学）
Federated learning (FL), which has gained increasing attention recently, enables distributed devices to train a common machine learning (ML) model for intelligent inference cooperatively without data sharing. However, problems in practical networks, such as non-independent-and-identically-distributed (non-iid) raw data and limited bandwidth, give rise to slow and unstable convergence of the FL training process. To address these issues, we propose a new FL method that can significantly mitigate statistical heterogeneity through the depersonalization mechanism. Particularly, we decouple the glob…
North China Electric Power University（华北电力大学）；Shandong University of Finance and Economics（山东财经大学）；Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）
Distributed privacy-preserving regression schemes have been developed and extended in various fields, where multiparty collaboratively and privately run optimization algorithms, e.g., Gradient Descent, to learn a set of optimal parameters. However, traditional Gradient-Descent based methods fail to solve problems which contains objective functions with L1 regularization, such as Lasso regression. In this paper, we present Federated Coordinate Descent, a new distributed scheme called FCD, to address this issue securely under multiparty scenarios. Specifically, through secure aggregation and add…
The University of Queensland（昆士兰大学）；Data61 CSIRO Australia（澳大利亚联邦科学与工业研究组织Data61）
Federated learning enables multiple participants to collaboratively train a model without aggregating the training data. Although the training data are kept within each participant and the local gradients can be securely synthesized, recent studies have shown that such privacy protection is insufficient. The global model parameters that have to be shared for optimization are susceptible to leak information about training data. In this work, we propose Confined Gradient Descent (CGD) that enhances privacy of federated learning by eliminating the sharing of global model parameters. CGD exploits …
Federated Unlearning with Gradient Descent and Conflict Mitigation
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Guangzhou University（广州大学）；The Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳人工智能与机器人研究院）；University of Michigan（密歇根大学）；Shenzhen Research Institute of Big Data（深圳大数据研究院）
Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods invariably rely on some form of acceleration/momentum to reduce the number of iterations, there are no methods which combine the benefits of both gradient compression and acceleration. In this paper, we remedy this situation and propose the first accelerated compressed gradient descent (ACGD) methods. In the single machine regime, we prove that ACGD enjoys t…
Guanghua School of Management, Peking University（北京大学光华管理学院）；Center for Applied Statistics, Renmin University of China（中国人民大学应用统计中心）；School of Statistics, Renmin University of China（中国人民大学统计学院）
We study a fully decentralized federated learning algorithm, which is a novel gradient descent algorithm executed on a communication-based network. For convenience, we refer to it as a network gradient descent (NGD) method. In the NGD method, only statistics (e.g., parameter estimates) need to be communicated, minimizing the risk of privacy. Meanwhile, different clients communicate with each other directly according to a carefully designed network structure without a central master. This greatly enhances the reliability of the entire algorithm. Those nice properties inspire us to carefully stu…
FedBCD:Communication-Efficient Accelerated Block Coordinate Gradient Descent for Federated Learning
School of Artificial Intelligence Xi'an Xidian University, China；College of Intelligence；Computing Tianjin Tianjin University, China；Medical College, Tianjin University\ Cheng Laboratory Tianjin China；University of Southern California Los Angeles US；School of Artificial Intelligence；Medical College, Tianjin University\ Cheng Laboratory；University of Southern California
We propose and analyze a new type of stochastic first order method: gradient descent with compressed iterates (GDCI). GDCI in each iteration first compresses the current iterate using a lossy randomized compression technique, and subsequently takes a gradient step. This method is a distillation of a key ingredient in the current practice of federated learning, where a model needs to be compressed by a mobile device before it is sent back to a server for aggregation. Our analysis provides a step towards closing the gap between the theory and practice of federated learning, and opens the possibi…
Samsung R&D Institute India – Bangalore（三星印度研发研究院 - 班加罗尔）；Birla Institute of Technology and Science（比尔拉理工学院）；Indian Statistical Institute（印度统计研究所）；Samsung Electronics（三星电子）
Federated Learning (FL) is a privacy preserving machine learning scheme, where training happens with data federated across devices and not leaving them to sustain user privacy. This is ensured by making the untrained or partially trained models to reach directly the individual devices and getting locally trained "on-device" using the device owned data, and the server aggregating all the partially trained model learnings to update a global model. Although almost all the model learning schemes in the federated learning setup use gradient descent, there are certain characteristic differences brou…
Changchun University of Science and Technology（长春理工大学）；Northeast Normal University（东北师范大学）
The plain stochastic gradient descent and momentum stochastic gradient descent have extremely wide applications in deep learning due to their simple settings and low computational complexity. The momentum stochastic gradient descent uses the accumulated gradient as the updated direction of the current parameters, which has a faster training speed. Because the direction of the plain stochastic gradient descent has not been corrected by the accumulated gradient. For the parameters that currently need to be updated, it is the optimal direction, and its update is more accurate. We combine the adva…
Peking University（北京大学）；Princeton University（普林斯顿大学）；The University of Washington（华盛顿大学）
Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradi…
Massachusetts Institute of Technology（麻省理工学院）；University of Oxford（牛津大学）
We study the hardness of learning unitary transformations in $U(d)$ via gradient descent on time parameters of alternating operator sequences. We provide numerical evidence that, despite the non-convex nature of the loss landscape, gradient descent always converges to the target unitary when the sequence contains $d^2$ or more parameters. Rates of convergence indicate a "computational phase transition." With less than $d^2$ parameters, gradient descent converges to a sub-optimal solution, whereas with more than $d^2$ parameters, gradient descent converges exponentially to an optimal solution.
We describe an alternative learning method for neural networks, which we call Blind Descent. By design, Blind Descent does not face problems like exploding or vanishing gradients. In Blind Descent, gradients are not used to guide the learning process. In this paper, we present Blind Descent as a more fundamental learning process compared to gradient descent. We also show that gradient descent can be seen as a specific case of the Blind Descent algorithm. We also train two neural network architectures, a multilayer perceptron and a convolutional neural network, using the most general Blind Desc…
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we run some computer experiments for gradient descent on some simple functions, and observe this principle in some concrete examples.
In high dimensions, most machine learning method perform fragile even there are a little outliers. To address this, we hope to introduce a new method with the base learner, such as Bayesian regression or stochastic gradient descent to solve the problem of the vulnerability in the model. Because the mini-batch gradient descent allows for a more robust convergence than the batch gradient descent, we work a method with the mini-batch gradient descent, called Mini-Batch Gradient Descent with Trimming (MBGDT). Our method show state-of-art performance and have greater robustness than several baselin…
With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving various optimization problems, due to its simple structure, good stability and easy implementation. In multi-node machine learning system, the gradients usually need to be shared. Shared gradients are generally unsafe. Attackers can obtain training data simply by knowing the gradient information. In this paper, to prevent gradient leakage while keeping the accuracy of model, we pr…
We consider the behavior of gradient flow and of discrete and noisy gradient descent. It is commonly noted that the addition of noise to the process of discrete gradient descent can affect the trajectory of gradient descent. In previous work, we observed such effects. There, we considered the case where the minima had codimension 1. In this note, we do some computer experiments and observe the behavior of noisy gradient descent in the more complex setting of minima of higher codimension.
As part of the effort to understand implicit bias of gradient descent in overparametrized models, several results have shown how the training trajectory on the overparametrized model can be understood as mirror descent on a different objective. The main result here is a characterization of this phenomenon under a notion termed commuting parametrization, which encompasses all the previous results in this setting. It is shown that gradient flow with any commuting parametrization is equivalent to continuous mirror descent with a related Legendre function. Conversely, continuous mirror descent wit…
Insight Centre for Data Analytics, NUI Galway（爱尔兰国立大学高威数据分析中心）；Aylien Ltd.（Aylien有限公司）
Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with intuitions with regard to the behaviour of different algorithms that will allow her to put them to use. In the course of this overview, we look at different variants of gradient descent, summarize challenges, introduce the most common optimization algorithms, review architectures in a parallel and distributed setting, and investigate additional strategies for op…
Most of the recent successful applications of neural networks have been based on training with gradient descent updates. However, for some small networks, other mirror descent updates learn provably more efficiently when the target is sparse. We present a general framework for casting a mirror descent update as a gradient descent update on a different set of parameters. In some cases, the mirror descent reparameterization can be described as training a modified network with standard backpropagation. The reparameterization framework is versatile and covers a wide range of mirror descent updates…
We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad range of derivative-free black-box functions, including Gaussian process bandits, simple control objectives, global optimization benchmarks and hyper-parameter tuning tasks. Up to the training horizon, the learned optimizers learn to trade-off exploration and exploitation, and compare favourably with heavily engineered Bayesian optimization packages for hyper…
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）
To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the more complicated inter-outer problem structure in federated min-max learning, theoretical understandings of communication complexity for federated min-max learning with infrequent communications remain very limited in the literature. This is particularly true for settings with non-i.i.d. datasets and partial client participation. To address this challenge, in t…
Non-convex optimization problems are challenging to solve; the success and computational expense of a gradient descent algorithm or variant depend heavily on the initialization strategy. Often, either random initialization is used or initialization rules are carefully designed by exploiting the nature of the problem class. As a simple alternative to hand-crafted initialization rules, we propose an approach for learning "good" initialization rules from previous solutions. We provide theoretical guarantees that establish conditions that are sufficient in all cases and also necessary in some unde…
There introduce Particle Optimized Gradient Descent (POGD), an algorithm based on the gradient descent but integrates the particle swarm optimization (PSO) principle to achieve the iteration. From the experiments, this algorithm has adaptive learning ability. The experiments in this paper mainly focus on the training speed to reach the target value and the ability to prevent the local minimum. The experiments in this paper are achieved by the convolutional neural network (CNN) image classification on the MNIST and cifar-10 datasets.
We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related gradient flow. We show that under suitable conditions on the step sizes gradient descent converges to a critical point of the loss function, i.e., the square loss in this article. Furthermore, we demonstrate that for almost all initializations gradient descent converges to a global minimum in the case of two layers. In the case of three or more layers we show that gradient descent converges to a global minimum on th…
This paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(lambda), LSTD(lambda), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms…
TTI at Chicago（芝加哥丰田理工学院）；USC（南加利福尼亚大学）；Technion（以色列理工学院）
We show that gradient descent on full-width linear convolutional networks of depth $L$ converges to a linear predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear support vector machine solution, regardless of depth.
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan and Kale [2012] with convergence rate $O\left(\frac{1}{\varepsilon^4}\right)$.
We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.
One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value of a function we need gradient. And to update our weights we need gradient descent. But there are some problems with regular gradient descent ie. it is quite slow and not that accurate. This article aims to give an introduction to optimization strategies to gradient descent. In addition, we shall also discuss the architecture of these algorithms and further…
In this work, we propose an optimization algorithm which we call norm-adapted gradient descent. This algorithm is similar to other gradient-based optimization algorithms like Adam or Adagrad in that it adapts the learning rate of stochastic gradient descent at each iteration. However, rather than using statistical properties of observed gradients, norm-adapted gradient descent relies on a first-order estimate of the effect of a standard gradient descent update step, much like the Newton-Raphson method in many dimensions. Our algorithm can also be compared to quasi-Newton methods, but we seek r…
Department of Computer Science, Stanford University（斯坦福大学计算机科学系）；Department of Computer Science, Columbia University（哥伦比亚大学计算机科学系）；Google Research, Mountain View（谷歌研究院（山景城））
We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in very simple learning settings. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradient descent.
Sorbonne Université（索邦大学）；Institut des Systèmes Intelligents et de Robotique（智能与机器人系统研究院）
In this paper, we provide an overview of first-order and second-order variants of the gradient descent method that are commonly used in machine learning. We propose a general framework in which 6 of these variants can be interpreted as different instances of the same approach. They are the vanilla gradient descent, the classical and generalized Gauss-Newton methods, the natural gradient descent method, the gradient covariance matrix approach, and Newton's method. Besides interpreting these methods within a single framework, we explain their specificities and show under which conditions some of…
In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient algorithms, has widely approximated stochastic gradient descent by a stochastic differential equation with Gaussian noise. We provide a novel rigorous theoretical justification for this practice that showcases how the Gaussianity of the noise arises naturally.
With a weighting scheme proportional to t, a traditional stochastic gradient descent (SGD) algorithm achieves a high probability convergence rate of O(κ/T) for strongly convex functions, instead of O(κ ln(T)/T). We also prove that an accelerated SGD algorithm also achieves a rate of O(κ/T).
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and converge to local minimizers [Lee et. al. 2016]. Recent studies also show a perturbed version of gradient descent is enough to escape saddle points efficiently [Jin et. al. 2015, Ge et. al. 2017]. In this paper we show a negative result: gradient descent may take exponential time to escape saddle points, with non-pathological two dimensional functions. While o…
