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We present CYCLADES, a general framework for parallelizing stochastic optimization algorithms in a shared memory setting. CYCLADES is asynchronous during shared model updates, and requires no memory locking mechanisms, similar to HOGWILD!-type algorithms. Unlike HOGWILD!, CYCLADES introduces no conflicts during the parallel execution, and offers a black-box analysis for provable speedups across a large family of algorithms. Due to its inherent conflict-free nature and cache locality, our multi-core implementation of CYCLADES consistently outperforms HOGWILD!-type algorithms on sufficiently sparse datasets, leading to up to 40% speedup gains compared to the HOGWILD! implementation of SGD, and up to 5x gains over asynchronous implementations of variance reduction algorithms.
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We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptions of previous models, and in some cases yield improved upper bounds on the convergence rates. We proceed to apply our framework to develop and analyze KroMagnon: a novel, parallel, sparse stochastic variance-reduced gradient (SVRG) algorithm. We demonstrate experimentally on a 16-core machine that the sparse and parallel version of SVRG is in some cases more than four orders of magnitude faster than the standard SVRG algorithm.
Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel of many applications, such as circuit simulators, computational fluid dynamics or structural analysis etc. The problem of designing approaches for parallelizing these computations, to get good speedups as much as possible as per Amdahls law, has been continuously researched upon. In this paper, we discuss approaches based on the use of finite projective geometry graphs for these two problems. For the problem of conjugate gradient algorithm, the approach looks at an alternative data distribution based on projective-geometry concepts. It is proved that this data distribution is an optimal data distribution for scheduling the main problem of dense matrix-vector multiplication. For the problem of parallel LU/Cholesky decomposition of general matrices, the approach is motivated by the recently published scheme for interconnects of distributed systems, perfect difference networks. We find that projective-geometry based graphs indeed offer an exciting way of parallelizing these computations, and in fact many others. Moreover, their applications ranges from architectural ones (interconnect choice) to algorithmic ones (data distributions).
Accurate predictions of reactive mixing are critical for many Earth and environmental science problems. To investigate mixing dynamics over time under different scenarios, a high-fidelity, finite-element-based numerical model is built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations are performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast, and molecular diffusion. Outputs comprise concentration profiles of the reactants and products. The inputs and outputs of these simulations are concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) emulators to approximate system behavior. The 20 ML emulators based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptron (MLP), are compared to assess these models. The ML emulators are specifically trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay, and degree of mixing. Linear classifiers and regressors fail to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP accurately classify the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predict the QoIs. At run time, trained ML emulators are $approx10^5$ times faster than the high-fidelity numerical simulations. Speed and accuracy of the ensemble and MLP models facilitate uncertainty quantification, which usually requires 1,000s of model run, to estimate the uncertainty bounds on the QoIs.
This paper considers the modeling and the analysis of the performance of lock-free concurrent data structures. Lock-free designs employ an optimistic conflict control mechanism, allowing several processes to access the shared data object at the same time. They guarantee that at least one concurrent operation finishes in a finite number of its own steps regardless of the state of the operations. Our analysis considers such lock-free data structures that can be represented as linear combinations of fixed size retry loops. Our main contribution is a new way of modeling and analyzing a general class of lock-free algorithms, achieving predictions of throughput that are close to what we observe in practice. We emphasize two kinds of conflicts that shape the performance: (i) hardware conflicts, due to concurrent calls to atomic primitives; (ii) logical conflicts, caused by simultaneous operations on the shared data structure. We show how to deal with these hardware and logical conflicts separately, and how to combine them, so as to calculate the throughput of lock-free algorithms. We propose also a common framework that enables a fair comparison between lock-free implementations by covering the whole contention domain, together with a better understanding of the performance impacting factors. This part of our analysis comes with a method for calculating a good back-off strategy to finely tune the performance of a lock-free algorithm. Our experimental results, based on a set of widely used concurrent data structures and on abstract lock-free designs, show that our analysis follows closely the actual code behavior.
Federated learning (FL) is an emerging distributed machine learning paradigm that protects privacy and tackles the problem of isolated data islands. At present, there are two main communication strategies of FL: synchronous FL and asynchronous FL. The advantages of synchronous FL are that the model has high precision and fast convergence speed. However, this synchronous communication strategy has the risk that the central server waits too long for the devices, namely, the straggler effect which has a negative impact on some time-critical applications. Asynchronous FL has a natural advantage in mitigating the straggler effect, but there are threats of model quality degradation and server crash. Therefore, we combine the advantages of these two strategies to propose a clustered semi-asynchronous federated learning (CSAFL) framework. We evaluate CSAFL based on four imbalanced federated datasets in a non-IID setting and compare CSAFL to the baseline methods. The experimental results show that CSAFL significantly improves test accuracy by more than +5% on the four datasets compared to TA-FedAvg. In particular, CSAFL improves absolute test accuracy by +34.4% on non-IID FEMNIST compared to TA-FedAvg.
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