Virtually all state-of-the-art methods for training supervised machine learning models are variants of SGD enhanced with a number of additional tricks, such as minibatching, momentum, and adaptive stepsizes. One of the tricks that works so well in practice that it is used as default in virtually all widely used machine learning software is {\em random reshuffling (RR)}. However, the practical benefits of RR have until very recently been eluding attempts at being satisfactorily explained using theory. Motivated by recent development due to Mishchenko, Khaled and Richtárik (2020), in this work we provide the first analysis of SVRG under Random Reshuffling (RR-SVRG) for general finite-sum problems. First, we show that RR-SVRG converges linearly with the rate $\mathcal{O}(κ^{3/2})$ in the strongly-convex case, and can be improved further to $\mathcal{O}(κ)$ in the big data regime (when $n > \mathcal{O}(κ)$), where $κ$ is the condition number. This improves upon the previous best rate $\mathcal{O}(κ^2)$ known for a variance reduced RR method in the strongly-convex case due to Ying, Yuan and Sayed (2020). Second, we obtain the first sublinear rate for general convex problems. Third, we establish similar fast rates for Cyclic-SVRG and Shuffle-Once-SVRG. Finally, we develop and analyze a more general variance reduction scheme for RR, which allows for less frequent updates of the control variate. We corroborate our theoretical results with suitably chosen experiments on synthetic and real datasets.
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Random Reshuffling (RR), which is a variant of Stochastic Gradient Descent (SGD) employing sampling without replacement, is an immensely popular method for training supervised machine learning models via empirical risk minimization. Due to its superior practical performance, it is embedded and often set as default in standard machine learning software. Under the name FedRR, this method was recently shown to be applicable to federated learning (Mishchenko et al.,2021), with superior performance when compared to common baselines such as Local SGD. Inspired by this development, we design three ne…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is usually faster in practice and enjoys significant popularity in convex and non-convex optimization. The convergence rate of RR has attracted substantial attention recently and, for strongly convex and smooth functions, it was shown to converge faster than SGD if 1) the stepsize is small, 2) the gradients are bounded, and 3) the number of epochs is large. We remo…
UCLA（加州大学洛杉矶分校）；Swiss Federal Institute of Technology (EPFL)（瑞士联邦理工学院（洛桑））
Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform data sampling with replacement. However, it has been observed in related works that random reshuffling can deliver superior performance over uniform sampling and, yet, no formal proofs or guarantees of exact convergence exist for variance-reduced algorithms under random reshuffling. This paper makes two contributions. First, it resolves this o…
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）
When solving finite-sum minimization problems, two common alternatives to stochastic gradient descent (SGD) with theoretical benefits are random reshuffling (SGD-RR) and shuffle-once (SGD-SO), in which functions are sampled in cycles without replacement. Under a convenient stochastic noise approximation which holds experimentally, we study the stationary variances of the iterates of SGD, SGD-RR and SGD-SO, whose leading terms decrease in this order, and obtain simple approximations. To obtain our results, we study the power spectral density of the stochastic gradient noise sequences. Our analy…
University of Pennsylvania（宾夕法尼亚大学）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）；Tsinghua University（清华大学）
When applying a stochastic algorithm, one must choose an order to draw samples. The practical choices are without-replacement sampling orders, which are empirically faster and more cache-friendly than uniform-iid-sampling but often have inferior theoretical guarantees. Without-replacement sampling is well understood only for SGD without variance reduction. In this paper, we will improve the convergence analysis and rates of variance reduction under without-replacement sampling orders for composite finite-sum minimization. Our results are in two-folds. First, we develop a damped variant of Fini…
In this work, we investigate the idea of variance reduction by studying its properties with general adaptive mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized framework for variance reduced adaptive mirror descent algorithms named SVRAMD and provide its convergence analysis in both the nonsmooth nonconvex problem and the P-L conditioned problem. We prove that variance reduction reduces the SFO complexity of adaptive mirror descent algorithms and thus accelerates their convergence. In particular, our general theory implies tha…
We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic gradient descent (SGD) based algorithms with variance reduction converge with a linear convergent rate on convex problems. However, there is no work to analyze asynchronous SGD with variance reduction technique on non-convex problem. In this paper, we study two asynchronous parallel implementations of SVRG: one is on a distributed memory system and the other is o…
University of California, Los Angeles（加州大学洛杉矶分校）；Ecole Polytechnique Federale de Lausanne (EPFL)（洛桑联邦理工学院）
A new amortized variance-reduced gradient (AVRG) algorithm was developed in \cite{ying2017convergence}, which has constant storage requirement in comparison to SAGA and balanced gradient computations in comparison to SVRG. One key advantage of the AVRG strategy is its amenability to decentralized implementations. In this work, we show how AVRG can be extended to the network case where multiple learning agents are assumed to be connected by a graph topology. In this scenario, each agent observes data that is spatially distributed and all agents are only allowed to communicate with direct neighb…
Adaptive Variance Reduction without Knowing Oracle Smoothness
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；National Key Laboratory for Novel Software Technology, Nanjing University（南京大学新型软件技术国家重点实验室）
Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large "mega-batches" in order to achieve their improved results. We present a new algorithm, STORM, that does not require any batches and makes use of adaptive learning rates, enabling simpler implementation and les…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for example by data augmentation. In such cases, the objective is no longer a finite sum, and the main candidate for optimization is the stochastic gradient descent method (SGD). In this paper, we introduce a variance reduction approach for these settings when the objective is composite and strongly convex. The convergence rate outperforms SGD with a typically much…
In the era of big data, optimizing large scale machine learning problems becomes a challenging task and draws significant attention. Asynchronous optimization algorithms come out as a promising solution. Recently, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD) is proposed to minimize a composite function. It is claimed to be able to off-loads the computation bottleneck from server to workers by allowing workers to evaluate the proximal operators, therefore, server just need to do element-wise operations. However, it still suffers from slow convergence rate because of the…
Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold. In this paper, we further improve on existing variance reduction methods for non-convex Riemannian optimization, including R-SVRG and R-SRG/R-SPIDER with batch size adaptation. We show that this strategy can achieve lower total complexities for optimizing both general non-convex and gradient dominated functions under both finite-sum and online settings. As a result, we also provide simpler convergence analy…
Composition optimization is widely-applied in nonconvex machine learning. Various advanced stochastic algorithms that adopt momentum and variance reduction techniques have been developed for composition optimization. However, these algorithms do not fully exploit both techniques to accelerate the convergence and are lack of convergence guarantee in nonconvex optimization. This paper complements the existing literature by developing various momentum schemes with SPIDER-based variance reduction for non-convex composition optimization. In particular, our momentum design requires less number of pr…
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical analysis of convergence in a non-convex setting and experimental results which demonstrate improved performance on a variety of machine learning areas including neural networks and black box variational inference. We also present a distributed version of our algorithm that enables large-dimensional optimization, and we extend our algorithm to SGD with momentum…
Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of semi-supervised node classification tasks. Despite their great success, training GCNs on large graphs suffers from computational and memory issues. A potential path to circumvent these obstacles is sampling-based methods, where at each layer a subset of nodes is sampled. Although recent studies have empirically demonstrated the effectiveness of sampling-based methods, these works lack theoretical convergence guarantees under realistic settings and cannot fully leverage the information of…
Tokyo Institute of Technology（东京工业大学）；Japan Science and Technology Agency（日本科学技术振兴机构）
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging method with variance reduction. Our methods generate a sparser solution than the existing methods because we do not need to take the average of the history of the solutions. This is favorable in terms of both interpretability and generalization. Moreover, our methods have theoretical support for both a strongly and a non-strongly convex regularizer and achie…
University of Maryland, College Park（马里兰大学帕克分校）；United States Naval Academy（美国海军学院）
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset) at the end of each epoch. This limits the use of VR methods in practical distributed settings. In this paper, we propose a variance reduction method, called VR-lite, that does not require full gradient computations or extra storage. We explore distributed synchronous and asynchr…
This paper proposes an algorithm (RMDA) for training neural networks (NNs) with a regularization term for promoting desired structures. RMDA does not incur computation additional to proximal SGD with momentum, and achieves variance reduction without requiring the objective function to be of the finite-sum form. Through the tool of manifold identification from nonlinear optimization, we prove that after a finite number of iterations, all iterates of RMDA possess a desired structure identical to that induced by the regularizer at the stationary point of asymptotic convergence, even in the presen…
Techniques for reducing the variance of gradient estimates used in stochastic programming algorithms for convex finite-sum problems have received a great deal of attention in recent years. By leveraging dissipativity theory from control, we provide a new perspective on two important variance-reduction algorithms: SVRG and its direct accelerated variant Katyusha. Our perspective provides a physically intuitive understanding of the behavior of SVRG-like methods via a principle of energy conservation. The tools discussed here allow us to automate the convergence analysis of SVRG-like methods by c…
The University of Sydney（悉尼大学）；University of California, Davis（加州大学戴维斯分校）
Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search direction from Gaussian distribution and compute the estimated gradient along that direction. However, due to the variance in the search direction, the convergence rates and query complexities of existing methods suffer from a factor of $d$, where $d$ is the problem dimension. In this paper, we introduce a novel Stochastic Zeroth-order method with Variance Red…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference points to construct a semi-stochastic gradient with diminishing variance in each iteration, our algorithm uses $K+1$ nested reference points to build a semi-stochastic gradient to further reduce its variance in each iteration. For smooth nonconvex functions, the proposed algorith…
The University of Electro-Communications（电气通信大学）；Tokyo University of Science（东京理科大学）
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multiple gradients are addressed with notions of retraction and vector transport. We present convergence analyses of R-SQN-VR on both non-convex and retraction-convex functions under retraction and vector transport operators. The proposed algorithm is evaluated on the Karcher mean compu…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Mila, Université de Montréal（蒙特利尔大学米拉研究所）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Princeton University（普林斯顿大学）
Gradient compression is a popular technique for improving communication complexity of stochastic first-order methods in distributed training of machine learning models. However, the existing works consider only with-replacement sampling of stochastic gradients. In contrast, it is well-known in practice and recently confirmed in theory that stochastic methods based on without-replacement sampling, e.g., Random Reshuffling (RR) method, perform better than ones that sample the gradients with-replacement. In this work, we close this gap in the literature and provide the first analysis of methods w…
Carnegie Mellon University（卡内基梅隆大学）；Massachusetts Institute of Technology（麻省理工学院）
We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchronous versions of these algorithms---a crucial requirement for modern large-scale applications---have not been studied. We bridge this gap by presenting a unifying framework for many variance reduction techniques. Subsequently, we propose an asynchronous algorithm grounded in our …
Carnegie Mellon University（卡内基梅隆大学）；Massachusetts Institute of Technology（麻省理工学院）
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convexity. In contrast, we prove non-asymptotic rates of convergence (to stationary points) of SVRG for nonconvex optimization, and show that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence t…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order non-convex optimization remain to be full gradient descent that converges in $O(1/\varepsilon)$ iterations for smooth objectives, and stochastic gradient descent that converges in $O(1/\varepsilon^2)$ iterations for objectives that are sum of smooth functions. We provide the first improvement in this line of research. Our result is based on the variance reduction tr…
Fudan University（复旦大学）；SUNY at Buffalo（纽约州立大学布法罗分校）
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently, SPOS avoids the particle-collapsing pitfall of SVGD. Nevertheless, variance reduction in SPOS has never been studied. In this paper, we bridge the gap by presenting several variance-reduction techniques for SPOS. Specifically, we propose three variants of variance-reduced SPOS,…
Peking University（北京大学）；Microsoft Research（微软研究院）；Fudan University（复旦大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Regularized empirical risk minimization (R-ERM) is an important branch of machine learning, since it constrains the capacity of the hypothesis space and guarantees the generalization ability of the learning algorithm. Two classic proximal optimization algorithms, i.e., proximal stochastic gradient descent (ProxSGD) and proximal stochastic coordinate descent (ProxSCD) have been widely used to solve the R-ERM problem. Recently, variance reduction technique was proposed to improve ProxSGD and ProxSCD, and the corresponding ProxSVRG and ProxSVRCD have better convergence rate. These proximal algori…
Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & …
Humans are able to accelerate their learning by selecting training materials that are the most informative and at the appropriate level of difficulty. We propose a framework for distributing deep learning in which one set of workers search for the most informative examples in parallel while a single worker updates the model on examples selected by importance sampling. This leads the model to update using an unbiased estimate of the gradient which also has minimum variance when the sampling proposal is proportional to the L2-norm of the gradient. We show experimentally that this method reduces …
In this paper we study a family of variance reduction methods with randomized batch size---at each step, the algorithm first randomly chooses the batch size and then selects a batch of samples to conduct a variance-reduced stochastic update. We give the linear convergence rate for this framework for composite functions, and show that the optimal strategy to achieve the optimal convergence rate per data access is to always choose batch size of 1, which is equivalent to the SAGA algorithm. However, due to the presence of cache/disk IO effect in computer architecture, the number of data access ca…
Laboratory for Information and Inference Systems (LIONS), EPFL（洛桑联邦理工学院信息与推理系统实验室）
We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs and heteroscedastic noise. We provide a general theoretical guarantee for TruVaR covering thes…
The practice of applying several local updates before aggregation across clients has been empirically shown to be a successful approach to overcoming the communication bottleneck in Federated Learning (FL). Such methods are usually implemented by having clients perform one or more epochs of local training per round while randomly reshuffling their finite dataset in each epoch. Data imbalance, where clients have different numbers of local training samples, is ubiquitous in FL applications, resulting in different clients performing different numbers of local updates in each round. In this work, …
We propose an adaptive variance-reduction method, called AdaSpider, for minimization of $L$-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fairly distinct, adaptive step-size schedule with the recursive stochastic path integrated estimator proposed in [Fang et al., 2018]. To our knowledge, Adaspider is the first parameter-free non-convex variance-reduction method in the sense that it does not require the knowledge of problem-dependent parameters, such as smoothness constant $L$, …
University of Vienna（维也纳大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Grenoble INP（格勒诺布尔国立理工学院）；LIG（格勒诺布尔信息学实验室）；Maastricht University（马斯特里赫特大学）
We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by pseudo-monotone, Lipschitz continuous operators. The main computational advantage of Tseng's algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our…
Approximating Martingale Process (AMP) is proven to be effective for variance reduction in reinforcement learning (RL) in specific cases such as Multiclass Queueing Networks. However, in the already proven cases, the state space is relatively small and all possible state transitions can be iterated through. In this paper, we consider systems in which state space is large and have uncertainties when considering state transitions, thus making AMP a generalized variance-reduction method in RL. Specifically, we will investigate the application of AMP in ride-hailing systems like Uber, where Proxim…
University of Utah（犹他大学）；University at Buffalo（布法罗大学）
Greedy-GQ is a value-based reinforcement learning (RL) algorithm for optimal control. Recently, the finite-time analysis of Greedy-GQ has been developed under linear function approximation and Markovian sampling, and the algorithm is shown to achieve an $ε$-stationary point with a sample complexity in the order of $\mathcal{O}(ε^{-3})$. Such a high sample complexity is due to the large variance induced by the Markovian samples. In this paper, we propose a variance-reduced Greedy-GQ (VR-Greedy-GQ) algorithm for off-policy optimal control. In particular, the algorithm applies the SVRG-based vari…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Linköping University（林雪平大学）
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and forward-reflected-backward methods both in Euclidean and Bregman setups. All proposed methods converge in the same setting as their deterministic counterparts and they either match or improve the best-known complexities for solving structured min-max problems. Our results reinforce the correspondence between variance reduction in variational inequalities and minimizat…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Pontificia Universidad Católica de Chile（智利天主教大学）
We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance reduction. In the cocoercive -- and more generally Lipschitz-monotone -- setup, our algorithm attains $ε$ norm of the operator with $\mathcal{O}(\frac{1}{ε^3})$ stochastic operator evaluations, which significantly improves over state of the art $\mathcal{O}(\frac{1}{ε^4})$ stochastic operator evaluations required for existing monotone inclusion solvers applie…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a non-asymptotic convergence analysis of our framework and derive computational and sample complexities for our algorithm to converge to an $ε$-stationary point in expectation. In addition, extensive experiments for a wide class of SMF formulations demonstrate that our framework consistently yields faster convergence and a more accurate output dictionary vis-à-v…
University of Minnesota Twin Cities（明尼苏达大学双城分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；Northwestern University（西北大学）
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence guarantees and optimal estimation accuracy in high dimensions. We further extend the proposed algorithm to an asynchronous parallel variant with a near linear speedup. Numerical experiments demonstrate the efficiency of our algorithm in terms of both parameter estimation and computational performance.
UC Berkeley（加州大学伯克利分校）；University of Washington（华盛顿大学）；OpenAI（开放人工智能研究中心）
Policy gradient methods have enjoyed great success in deep reinforcement learning but suffer from high variance of gradient estimates. The high variance problem is particularly exasperated in problems with long horizons or high-dimensional action spaces. To mitigate this issue, we derive a bias-free action-dependent baseline for variance reduction which fully exploits the structural form of the stochastic policy itself and does not make any additional assumptions about the MDP. We demonstrate and quantify the benefit of the action-dependent baseline through both theoretical analysis as well as…
Instability and variability of Deep Reinforcement Learning (DRL) algorithms tend to adversely affect their performance. Averaged-DQN is a simple extension to the DQN algorithm, based on averaging previously learned Q-values estimates, which leads to a more stable training procedure and improved performance by reducing approximation error variance in the target values. To understand the effect of the algorithm, we examine the source of value function estimation errors and provide an analytical comparison within a simplified model. We further present experiments on the Arcade Learning Environmen…
Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an $ε$-second-order stationary point using only $\widetilde{O}(n^{2/3}/ε^2+n/ε^{1.5})$ stochastic gradients. To our best knowledge, this is the fir…
Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work addresses this gap and proposes Byz-VR-MARINA - a new Byzantine-tolerant method with variance reduction and compression. A key message of our paper is that variance reduction is key to fighting Byzantine workers more effectively. At the same time, communica…
École Polytechnique（巴黎综合理工学院）；HSE University（俄罗斯国立高等经济大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）
Policy-gradient methods in Reinforcement Learning(RL) are very universal and widely applied in practice but their performance suffers from the high variance of the gradient estimate. Several procedures were proposed to reduce it including actor-critic(AC) and advantage actor-critic(A2C) methods. Recently the approaches have got new perspective due to the introduction of Deep RL: both new control variates(CV) and new sub-sampling procedures became available in the setting of complex models like neural networks. The vital part of CV-based methods is the goal functional for the training of the CV…
