Stochastic Gradient Compression for Federated Learning over Wireless Network

As a mature distributed machine learning paradigm,federated learning enables wireless edge devices to collaboratively train a shared AI-model by stochastic gradient descent(SGD).However,devices need to upload high-dimensional stochastic gradients to edge server in training,which cause severe communication bottleneck.To address this problem,we compress the communication by sparsifying and quantizing the stochastic gradients of edge devices.We first derive a closed form of the communication compression in terms of sparsification and quantization factors.Then,the convergence rate of this communicationcompressed system is analyzed and several insights are obtained.Finally,we formulate and deal with the quantization resource allocation problem for the goal of minimizing the convergence upper bound,under the constraint of multiple-access channel capacity.Simulations show that the proposed scheme outperforms the benchmarks.

L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous process.Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes.Machine learning models have become key players in automating brain tumor detection.Gradient descent methods are the mainstream algorithms for solving machine learning models.In this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor detection.Firstly,the smooth hinge loss is introduced to be used as the loss function of SVM.It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization.Secondly,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the model.Finally,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth SVM.Distributed computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of data.The DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core resources.Due to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence speed.From the perspective of loss reduction,DPGD converges faster than PGD.The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection.Frompre-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Outage Probability Analysis for D2D-Enabled Heterogeneous Cellular Networks with Exclusion Zone:A Stochastic Geometry Approach

Interference management is one of the most important issues in the device-to-device(D2D)-enabled heterogeneous cellular networks(HetCNets)due to the coexistence of massive cellular and D2D devices in which D2D devices reuse the cellular spectrum.To alleviate the interference,an efficient interference management way is to set exclusion zones around the cellular receivers.In this paper,we adopt a stochastic geometry approach to analyze the outage probabilities of cellular and D2D users in the D2D-enabled HetCNets.The main difficulties contain three aspects:1)how to model the location randomness of base stations,cellular and D2D users in practical networks;2)how to capture the randomness and interrelation of cellular and D2D transmissions due to the existence of random exclusion zones;3)how to characterize the different types of interference and their impacts on the outage probabilities of cellular and D2D users.We then run extensive Monte-Carlo simulations which manifest that our theoretical model is very accurate.

Feasibility of stochastic gradient boosting approach for predicting rockburst damage in burst-prone mines

The database of 254 rockburst events was examined for rockburst damage classification using stochastic gradient boosting （SGB） methods. Five potentially relevant indicators including the stress condition factor, the ground support system capacity, the excavation span, the geological structure and the peak particle velocity of rockburst sites were analyzed. The performance of the model was evaluated using a 10 folds cross-validation （CV） procedure with 80%of original data during modeling, and an external testing set （20%） was employed to validate the prediction performance of the SGB model. Two accuracy measures for multi-class problems were employed： classification accuracy rate and Cohen’s Kappa. The accuracy analysis together with Kappa for the rockburst damage dataset reveals that the SGB model for the prediction of rockburst damage is acceptable.

求解一类非光滑凸优化问题的相对加速SGD算法

一阶优化算法由于其计算简单、代价小,被广泛应用于机器学习、大数据科学、计算机视觉等领域,然而,现有的一阶算法大多要求目标函数具有Lipschitz连续梯度,而实际中的很多应用问题不满足该要求。在经典的梯度下降算法基础上,引入随机和加速,提出一种相对加速随机梯度下降算法。该算法不要求目标函数具有Lipschitz连续梯度,而是通过将欧氏距离推广为Bregman距离,从而将Lipschitz连续梯度条件减弱为相对光滑性条件。相对加速随机梯度下降算法的收敛性与一致三角尺度指数有关,为避免调节最优一致三角尺度指数参数的工作量,给出一种自适应相对加速随机梯度下降算法。该算法可自适应地选取一致三角尺度指数参数。对算法收敛性的理论分析表明,算法迭代序列的目标函数值收敛于最优目标函数值。针对Possion反问题和目标函数的Hessian阵算子范数随变量范数多项式增长的极小化问题的数值实验表明,自适应相对加速随机梯度下降算法和相对加速随机梯度下降算法的收敛性能优于相对随机梯度下降算法。

Efficient and High-quality Recommendations via Momentum-incorporated Parallel Stochastic Gradient Descent-Based Learning

A recommender system(RS)relying on latent factor analysis usually adopts stochastic gradient descent(SGD)as its learning algorithm.However,owing to its serial mechanism,an SGD algorithm suffers from low efficiency and scalability when handling large-scale industrial problems.Aiming at addressing this issue,this study proposes a momentum-incorporated parallel stochastic gradient descent(MPSGD)algorithm,whose main idea is two-fold:a)implementing parallelization via a novel datasplitting strategy,and b)accelerating convergence rate by integrating momentum effects into its training process.With it,an MPSGD-based latent factor(MLF)model is achieved,which is capable of performing efficient and high-quality recommendations.Experimental results on four high-dimensional and sparse matrices generated by industrial RS indicate that owing to an MPSGD algorithm,an MLF model outperforms the existing state-of-the-art ones in both computational efficiency and scalability.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

CONVERGENCE OF ONLINE GRADIENT METHOD WITH A PENALTY TERM FOR FEEDFORWARD NEURAL NETWORKS WITH STOCHASTIC INPUTS

Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.

FL-EASGD:Federated Learning Privacy Security Method Based on Homomorphic Encryption

Federated learning ensures data privacy and security by sharing models among multiple computing nodes instead of plaintext data.However,there is still a potential risk of privacy leakage,for example,attackers can obtain the original data through model inference attacks.Therefore,safeguarding the privacy of model parameters becomes crucial.One proposed solution involves incorporating homomorphic encryption algorithms into the federated learning process.However,the existing federated learning privacy protection scheme based on homomorphic encryption will greatly reduce the efficiency and robustness when there are performance differences between parties or abnormal nodes.To solve the above problems,this paper proposes a privacy protection scheme named Federated Learning-Elastic Averaging Stochastic Gradient Descent(FL-EASGD)based on a fully homomorphic encryption algorithm.First,this paper introduces the homomorphic encryption algorithm into the FL-EASGD scheme to preventmodel plaintext leakage and realize privacy security in the process ofmodel aggregation.Second,this paper designs a robust model aggregation algorithm by adding time variables and constraint coefficients,which ensures the accuracy of model prediction while solving performance differences such as computation speed and node anomalies such as downtime of each participant.In addition,the scheme in this paper preserves the independent exploration of the local model by the nodes of each party,making the model more applicable to the local data distribution.Finally,experimental analysis shows that when there are abnormalities in the participants,the efficiency and accuracy of the whole protocol are not significantly affected.

Differentially private SGD with random features

In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance.Additionally,since the collected data may contain some sensitive information,it is also of great significance to study privacy-preserving machine learning algorithms.This paper focuses on the performance of the differentially private stochastic gradient descent(SGD)algorithm based on random features.To begin,the algorithm maps the original data into a lowdimensional space,thereby avoiding the traditional kernel method for large-scale data storage requirement.Subsequently,the algorithm iteratively optimizes parameters using the stochastic gradient descent approach.Lastly,the output perturbation mechanism is employed to introduce random noise,ensuring algorithmic privacy.We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions.

Auxiliary Model Based Multi-innovation Stochastic Gradient Identification Methods for Hammerstein Output-Error System

Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.

Predicted Oil Recovery Scaling-Law Using Stochastic Gradient Boosting Regression Model

In the process of oil recovery,experiments are usually carried out on core samples to evaluate the recovery of oil,so the numerical data are fitted into a non-dimensional equation called scaling-law.This will be essential for determining the behavior of actual reservoirs.The global non-dimensional time-scale is a parameter for predicting a realistic behavior in the oil field from laboratory data.This non-dimensional universal time parameter depends on a set of primary parameters that inherit the properties of the reservoir fluids and rocks and the injection velocity,which dynamics of the process.One of the practical machine learning(ML)techniques for regression/classification problems is gradient boosting(GB)regression.The GB produces a prediction model as an ensemble of weak prediction models that can be done at each iteration by matching a least-squares base-learner with the current pseudoresiduals.Using a randomization process increases the execution speed and accuracy of GB.Hence in this study,we developed a stochastic regression model of gradient boosting(SGB)to forecast oil recovery.Different nondimensional time-scales have been used to generate data to be used with machine learning techniques.The SGB method has been found to be the best machine learning technique for predicting the non-dimensional time-scale,which depends on oil/rock properties.

Stochastic Gradient Boosting Model for Twitter Spam Detection

In today’s world of connectivity there is a huge amount of data than we could imagine.The number of network users are increasing day by day and there are large number of social networks which keeps the users connected all the time.These social networks give the complete independence to the user to post the data either political,commercial or entertainment value.Some data may be sensitive and have a greater impact on the society as a result.The trustworthiness of data is important when it comes to public social networking sites like facebook and twitter.Due to the large user base and its openness there is a huge possibility to spread spam messages in this network.Spam detection is a technique to identify and mark data as a false data value.There are lot of machine learning approaches proposed to detect spam in social networks.The efficiency of any spam detection algorithm is determined by its cost factor and accuracy.Aiming to improve the detection of spam in the social networks this study proposes using statistical based features that are modelled through the supervised boosting approach called Stochastic gradient boosting to evaluate the twitter data sets in the English language.The performance of the proposed model is evaluated using simulation results.

Stochastic Finite Element Method for Mechanical Vibration Based on Conjugate Gradient(CG)

When material properties, geometry parameters and applied loads are assumed to be stochastic, the vibration equation of a system is transformed to static problem by using Newmark method. In order to improve the computational efficiency and to save storage, the Conjugate Gradient （CG） method is presented. The CG is an effective method for solving a large system of linear equations and belongs to the method of iteration with rapid convergence and high precision. An example is given and calculated results are compared to validate the proposed methods.

Online distributed optimization with stochastic gradients:high probability bound of regrets

In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.

A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

A Stochastic Approximation Frame Algorithm with Adaptive Directions

Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro （RM） algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a flame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criterions. Two feasible choices of the criterions are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.

基于SGDM优化IWOA-CNN的配电网工程造价控制研究

为了控制配电网工程项目的成本,需准确预测配电网工程造价,本文提出一种基于带动量因子的随机梯度下降(stochastic gradient descent with momentum factor, SGDM)优化的改进鲸鱼算法-卷积神经网络工程造价预测模型。首先,考虑回路数、杆塔数、导线、地形、地质、风速、覆冰、导线截面、混凝土杆、塔材、绝缘子(直线)、绝缘子(耐张)、基坑开方、基础钢材、底盘和水泥对配电网工程造价的影响,建立了非线性函数关系;采用SGDM优化器改进的卷积神经网络对函数进行逼近,并用贝叶斯方法优化卷积神经网络的超参数;利用改进的鲸鱼算法(improved whale optimization algorithm, IWOA)优化卷积神经网络,找出卷积神经网络的最优学习率。数值算例表明,新模型预测效果较好,并提出相应的控制策略。