In prior works, stochastic dual coordinate ascent (SDCA) has been parallelized in a multi-core environment where the cores communicate through shared memory, or in a multi-processor distributed memory environment where the processors communicate through message passing. In this paper, we propose a hybrid SDCA framework for multi-core clusters, the most common high performance computing environment that consists of multiple nodes each having multiple cores and its own shared memory. We distribute data across nodes where each node solves a local problem in an asynchronous parallel fashion on its cores, and then the local updates are aggregated via an asynchronous across-node update scheme. The proposed double asynchronous method converges to a global solution for @math -Lipschitz continuous loss functions, and at a linear convergence rate if a smooth convex loss function is used. Extensive empirical comparison has shown that our algorithm scales better than the best known shared-memory methods and runs faster than previous distributed-memory methods. Big datasets, such as one of 280 GB from the LIBSVM repository, cannot be accommodated on a single node and hence cannot be solved by a parallel algorithm. For such a dataset, our hybrid algorithm takes 30 seconds to achieve a duality gap of @math on 16 nodes each using 8 cores, which is significantly faster than the best known distributed algorithms, such as CoCoA+, that take more than 300 seconds on 16 nodes.
Besides distributed DCA methods, there are several recent distributed versions of other algorithms with faster convergence, including distributed Newton-type methods (DISCO @cite_15 , DANE @cite_18 ) and distributed stochastic variance reduced gradient method (DSVRG @cite_21 ). It has been shown that they can achieve the same accurate solution using fewer rounds of communication, however, with additional computational overhead. In particular, DISCO and DANE need to solve a linear system in each round, which could be very expensive for higher dimensions. DSVRG requires each machine to load and store a second subset of the data sampled from the original training data, which also increase its running time.
@cite_15 @cite_21 @cite_18
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Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked good convergence analysis. This paper presents a new analysis of Stochastic Dual Coordinate Ascent (SDCA) showing that this class of methods enjoy strong theoretical guarantees that are comparable or better than SGD. This analysis justifies the effectiveness of SDCA for practical applications. Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked good convergence analysis. This paper presents a new analysis of Stochastic Dual Coordinate Ascent (SDCA) showing that this class of methods enjoy strong theoretical guarantees that are comparable or better than SGD. This analysis justifies the effectiveness of SDCA for practical applications. Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g. SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1 T ) as opposed to O(1 T 2 ) of accelerated batch algorithms, where T is the number of iterations. Thus, there still remains a gap in convergence rates between existing stochastic ADMM and batch algorithms. To bridge this gap, we introduce the momentum acceleration trick for batch optimization into the stochastic variance reduced gradient based ADMM (SVRG-ADMM), which leads to an accelerated (ASVRG-ADMM) method. Then we design two different momentum term update rules for strongly convex and general convex cases. We prove that ASVRG-ADMM converges linearly for strongly convex problems. Besides having a low-iteration complexity as existing stochastic ADMM methods, ASVRG-ADMM improves the convergence rate on general convex problems from O(1 T ) to O(1 T 2 ). Our experimental results show the effectiveness of ASVRG-ADMM.