This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of {\em straggling} processors. To mitigate the effect of the stragglers, it has been previously proposed to encode the data with an erasure-correcting code and decode at the master server at the end of the computation. We, instead, propose to encode the second-moment of the data with a low density parity-check (LDPC) code. The iterative decoding algorithms for LDPC codes have very low computational overhead and the number of decoding iterations can be made to automatically adjust with the number of stragglers in the system. We show that for a random model for stragglers, the proposed moment encoding based gradient descent method can be viewed as the stochastic gradient descent method. This allows us to obtain convergence guarantees for the proposed solution. Furthermore, the proposed moment encoding based method is shown to outperform the existing schemes in a real distributed computing setup.
In many domains, the previous decade was characterized by increasing data volumes and growing complexity of computational workloads, creating new demands for highly data-parallel computing in distributed systems. Effective operation of these systems is challenging when facing uncertainties about the performance of jobs and tasks under varying resource configurations, e.g., for scheduling and resource allocation. We survey predictive performance modeling (PPM) approaches to estimate performance metrics such as execution duration, required memory or wait times of future jobs and tasks based on past performance observations. We focus on non-intrusive methods, i.e., methods that can be applied to any workload without modification, since the workload is usually a black-box from the perspective of the systems managing the computational infrastructure. We classify and compare sources of performance variation, predicted performance metrics, required training data, use cases, and the underlying prediction techniques. We conclude by identifying several open problems and pressing research needs in the field.
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregation process. We first prove the inconsistency of typical aggregations using disjoint or random data partition, and then present a consistent yet efficient aggregation model for large-scale GP. The proposed model inherits the advantages of aggregations, e.g., closed-form inference and aggregation, parallelization and distributed computing. Furthermore, theoretical and empirical analyses reveal that the new aggregation model performs better due to the consistent predictions that converge to the true underlying function when the training size approaches infinity.
We prove the existence of a semilinear representation of Cellular Automata (CA) with the introduction of multiple convolution kernels. Examples of the technique are presented for rules akin to the "edge-of-chaos" including the Turing universal rule 110 for further utilization in the area of reservoir computing. We also examine the significance of their dual representation on a frequency or wavelength domain as a superposition of plane waves for distributed computing applications including a new proposal for a "Hologrid" that could be realized with present Wi-Fi,Li-Fi technologies.