Distributed matrix computations over large clusters can suffer from the problem of slow or failed worker nodes (called stragglers) which can dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of stragglers by running 'coded' copies of tasks comprising a job; stragglers are typically treated as erasures. While this is useful, there are issues with applying, e.g., MDS codes in a straightforward manner. Several practical matrix computation scenarios involve sparse matrices. MDS codes typically require dense linear combinations of submatrices of the original matrices which destroy their inherent sparsity. This is problematic as it results in significantly higher worker computation times. Moreover, treating slow nodes as erasures ignores the potentially useful partial computations performed by them. Furthermore, some MDS techniques also suffer from significant numerical stability issues. In this work we present schemes that allow us to leverage partial computation by stragglers while imposing constraints on the level of coding that is required in generating the encoded submatrices. This significantly reduces the worker computation time as compared to previous approaches and results in improved numerical stability in the decoding process. Exhaustive numerical experiments on Amazon Web Services (AWS) clusters support our findings.
While performing distributed computations in today's cloud-based platforms, execution speed variations among compute nodes can significantly reduce the performance and create bottlenecks like stragglers. Coded computation techniques leverage coding theory to inject computational redundancy and mitigate stragglers in distributed computations. In this paper, we propose a dynamic workload distribution strategy for coded computation called Slack Squeeze Coded Computation ($S^2C^2$). $S^2C^2$ squeezes the compute slack (i.e., overhead) that is built into the coded computing frameworks by efficientl…
In distributed computing systems slow working nodes, known as stragglers, can greatly extend finishing times. Coded computing is a technique that enables straggler-resistant computation. Most coded computing techniques presented to date provide robustness by ensuring that the time to finish depends only on a set of the fastest nodes. However, while stragglers do compute less work than non-stragglers, in real-world commercial cloud computing systems (e.g., Amazon's Elastic Compute Cloud (EC2)) the distinction is often a soft one. In this paper, we develop hierarchical coded computing that explo…
Matrix factorization is an important representation learning algorithm, e.g., recommender systems, where a large matrix can be factorized into the product of two low dimensional matrices termed as latent representations. This paper investigates the problem of matrix factorization in distributed computing systems with stragglers, those compute nodes that are slow to return computation results. A computation procedure, called coded Alternative Least Square (ALS), is proposed for mitigating the effect of stragglers in such systems. The coded ALS algorithm iteratively computes two low dimensional …
In distributed computing systems, it is well recognized that worker nodes that are slow (called stragglers) tend to dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of stragglers by running "coded" copies of tasks comprising a job. Stragglers are typically treated as erasures in this process. While this is useful, there are issues with applying, e.g., MDS codes in a straightforward manner. Specifically, several applications such as matrix-vector products deal with sparse matrices. MDS codes typically require dense linear co…
Elasticity is offered by cloud service providers to exploit under-utilized computing resources. The low-cost elastic nodes can leave and join any time during the computation cycle. The possibility of elastic events occurring together with the problem of slow nodes, referred to as stragglers, increases the uncertainty of the system, leading to computation delay. Recent results have shown that coded computing can be used to reduce the negative effect of elasticity and stragglers. In this paper, we propose two hierarchical coded elastic computing schemes that can further speed up the system by ex…
Simula UiB；Chalmers University of Technology（查尔姆斯理工大学）
We present two novel federated learning (FL) schemes that mitigate the effect of straggling devices by introducing redundancy on the devices' data across the network. Compared to other schemes in the literature, which deal with stragglers or device dropouts by ignoring their contribution, the proposed schemes do not suffer from the client drift problem. The first scheme, CodedPaddedFL, mitigates the effect of stragglers while retaining the privacy level of conventional FL. It combines one-time padding for user data privacy with gradient codes to yield straggler resiliency. The second scheme, C…
The overall execution time of distributed matrix computations is often dominated by slow worker nodes (stragglers) within the clusters. Recently, different coding techniques have been utilized to mitigate the effect of stragglers where worker nodes are assigned the job of processing encoded submatrices of the original matrices. In many machine learning or optimization problems the relevant matrices are often sparse. Several prior coded computation methods operate with dense linear combinations of the original submatrices; this can significantly increase the worker node computation times and co…
Flexible Coded Distributed Convolution Computing for Enhanced Straggler Resilience and Numerical Stability in Distributed CNNs
College of Computer Science, Chongqing University（重庆大学计算机学院）；School of Electrical Engineering, Korea University（韩国大学电气工程学院）；School of Electronic Information and Communications, Huazhong University of Science and Technology（华中科技大学电子信息与通信学院）；City University of Hong Kong（香港城市大学）
Department of Electrical Engineering, University of Southern California（南加州大学电气工程系（University of Southern California 为南加州大学））
We consider the problem of training a least-squares regression model on a large dataset using gradient descent. The computation is carried out on a distributed system consisting of a master node and multiple worker nodes. Such distributed systems are significantly slowed down due to the presence of slow-running machines (stragglers) as well as various communication bottlenecks. We propose "polynomially coded regression" (PCR) that substantially reduces the effect of stragglers and lessens the communication burden in such systems. The key idea of PCR is to encode the partial data stored at each…
Coded computation is a method to mitigate "stragglers" in distributed computing systems through the use of error correction coding that has lately received significant attention. First used in vector-matrix multiplication, the range of application was later extended to include matrix-matrix multiplication, heterogeneous networks, convolution, and approximate computing. A drawback to previous results is they completely ignore work completed by stragglers. While stragglers are slower compute nodes, in many settings the amount of work completed by stragglers can be non-negligible. Thus, in this w…
One of the major challenges in using distributed learning to train complicated models with large data sets is to deal with stragglers effect. As a solution, coded computation has been recently proposed to efficiently add redundancy to the computation tasks. In this technique, coding is used across data sets, and computation is done over coded data, such that the results of an arbitrary subset of worker nodes with a certain size are enough to recover the final results. The major challenges with those approaches are (1) they are limited to polynomial function computations, (2) the size of the su…
We consider a status update system in which the update packets need to be processed to extract the embedded useful information. The source node sends the acquired information to a computation unit (CU) which consists of a master node and $n$ worker nodes. The master node distributes the received computation task to the worker nodes. Upon computation, the master node aggregates the results and sends them back to the source node to keep it \emph{updated}. We investigate the age performance of uncoded and coded (repetition coded, MDS coded, and multi-message MDS (MM-MDS) coded) schemes in the pre…
In cloud computing systems slow processing nodes, often referred to as "stragglers", can significantly extend the computation time. Recent results have shown that error correction coding can be used to reduce the effect of stragglers. In this work we introduce a scheme that, in addition to using error correction to distribute mixed jobs across nodes, is also able to exploit the work completed by all nodes, including stragglers. We first consider vector-matrix multiplication and apply maximum distance separable (MDS) codes to small blocks of sub-matrices. The worker nodes process blocks sequent…
We propose a serverless computing mechanism for distributed computation based on polar codes. Serverless computing is an emerging cloud based computation model that lets users run their functions on the cloud without provisioning or managing servers. Our proposed approach is a hybrid computing framework that carries out computationally expensive tasks such as linear algebraic operations involving large-scale data using serverless computing and does the rest of the processing locally. We address the limitations and reliability issues of serverless platforms such as straggling workers using codi…
Slow working nodes, known as stragglers, can greatly reduce the speed of distributed computation. Coded matrix multiplication is a recently introduced technique that enables straggler-resistant distributed multiplication of large matrices. A key property is that the finishing time depends only on the work completed by a set of the fastest workers, while the work done by the slowest workers is ignored completely. This paper is motivated by the observation that in real-world commercial cloud computing systems such as Amazon's Elastic Compute Cloud (EC2) the distinction between fast and slow node…
We consider the problem of computing the convolution of two long vectors using parallel processing units in the presence of "stragglers". Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides better resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can drama…
Computationally intensive distributed and parallel computing is often bottlenecked by a small set of slow workers known as stragglers. In this paper, we utilize the emerging idea of "coded computation" to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative methods in a parallelized implementation affected by stragglers. Example applications include inverse problems in machine learning on graphs, such as personalized PageRank and sampling on graphs. We provably show that our coded-computation technique can reduce the mean-squared …
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst processors in coded matrix multiplication as a cuboid partitioning problem. This framework allows us to unify existing methods and motivates new techniques. Building on this framework, we apply the idea of hierarchical coding (Ferdinand & Draper, 2018) to coded matrix multiplication. The hierarchical scheme we develop is able to exploit the work completed by al…
Our extensive real measurements over Amazon EC2 show that the virtual instances often have different computing speeds even if they share the same configurations. This motivates us to study heterogeneous Coded Storage Elastic Computing (CSEC) systems where machines, with different computing speeds, join and leave the network arbitrarily over different computing steps. In CSEC systems, a Maximum Distance Separable (MDS) code is used for coded storage such that the file placement does not have to be redefined with each elastic event. Computation assignment algorithms are used to minimize the comp…
The current BigData era routinely requires the processing of large scale data on massive distributed computing clusters. Such large scale clusters often suffer from the problem of "stragglers", which are defined as slow or failed nodes. The overall speed of a computational job on these clusters is typically dominated by stragglers in the absence of a sophisticated assignment of tasks to the worker nodes. In recent years, approaches based on coding theory (referred to as "coded computation") have been effectively used for straggler mitigation. Coded computation offers significant benefits for s…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency caused by individual processors ("stragglers") usually causes a significant delay in the overall process. The proposed method is powered by a sequential computation scheme, which is designed specifically for systems with stragglers. This scheme has the desirable property that the user is guaranteed to receive useful (approximate) computation results whenever …
A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single computation task and batch processing of multiple distinct computation tasks. While these works provide codes with good straggler resilience and fast decoding for their problem spaces, these codes would not be able to take advantage of the natural redundancy of re-using matrices across batch jobs. In this paper, we introduce the Variable Coded Distributed Batch Matrix Multiplication (VCDBMM) problem which tasks a distributed system to perform batch matrix m…
University of Southern California（南加州大学）；Nokia Bell Labs（诺基亚贝尔实验室）
We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs. We show that by exploiting the algebraic structure of the Fourier transform operation and leveraging concepts from coding theory, one can efficiently deal with the straggler effects. In particular, we propose a computation strategy, named as coded FFT, which achieves the optimal recovery threshold, defined as the minimum number of workers…
Faced with saturation of Moore's law and increasing dimension of data, system designers have increasingly resorted to parallel and distributed computing. However, distributed computing is often bottle necked by a small fraction of slow processors called "stragglers" that reduce the speed of computation because the fusion node has to wait for all processors to finish. To combat the effect of stragglers, recent literature introduces redundancy in computations across processors, e.g.,~using repetition-based strategies or erasure codes. The fusion node can exploit this redundancy by completing the…
We consider the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. For this framework, we propose the use of binary matrices (with $0,1$ entries) called \textit{computing matrices} to describe the map phase and the shuffle phase. Similar binary matrices were recently proposed for the coded caching framework. The structure of ones and zeroes in the binary computing matrix captures the map phase of the MapReduce framework. We present a new simple coded data shuffling scheme for this binary matrix model, based on a …
University of Southern California（南加利福尼亚大学）；California Institute of Technology（加利福尼亚理工学院）
We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create compu…
Purdue University（普渡大学）；Iowa State University（爱荷华州立大学）
Federated learning (FL) is a popular technique for training a global model on data distributed across client devices. Like other distributed training techniques, FL is susceptible to straggler (slower or failed) clients. Recent work has proposed to address this through device-to-device (D2D) offloading, which introduces privacy concerns. In this paper, we propose a novel straggler-optimal approach for coded matrix computations which can significantly reduce the communication delay and privacy issues introduced from D2D data transmissions in FL. Moreover, our proposed approach leads to a consid…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded computation strategy, referred to as diagonal code, that achieves the optimum recovery threshold and the optimum computation load. This is the first code that simultaneously achieves two-fold optimality in coded distributed linear transforms. Furthermore, by leveraging the idea from random proposal graph theory, we design two random codes that can guarantee o…
Imperial College London（伦敦帝国学院）；University of Maryland, College Park（马里兰大学帕克分校）
Distributed gradient descent (DGD) is an efficient way of implementing gradient descent (GD), especially for large data sets, by dividing the computation tasks into smaller subtasks and assigning to different computing servers (CSs) to be executed in parallel. In standard parallel execution, per-iteration waiting time is limited by the execution time of the straggling servers. Coded DGD techniques have been introduced recently, which can tolerate straggling servers via assigning redundant computation tasks to the CSs. In most of the existing DGD schemes, either with coded computation or coded …
We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage constraints. In approximate nearest neighbor algorithms, it is common to construct efficient in-memory indexes to improve query response time. One such strategy is Multiple Random Projection Trees (MRPT), which reduces the set of candidate points over which Euclidean distance calculations are performed. However, this may result in a high memory footprint an…
Large-scale distributed computing systems face two major bottlenecks that limit their scalability: straggler delay caused by the variability of computation times at different worker nodes and communication bottlenecks caused by shuffling data across many nodes in the network. Recently, it has been shown that codes can provide significant gains in overcoming these bottlenecks. In particular, optimal coding schemes for minimizing latency in distributed computation of linear functions and mitigating the effect of stragglers was proposed for a wired network, where the workers can simultaneously tr…
Runtime performance variability at the servers has been a major issue, hindering the predictable and scalable performance in modern distributed systems. Executing requests or jobs redundantly over multiple servers has been shown to be effective for mitigating variability, both in theory and practice. Systems that employ redundancy has drawn significant attention, and numerous papers have analyzed the pain and gain of redundancy under various service models and assumptions on the runtime variability. This paper presents a cost (pain) vs. latency (gain) analysis of executing jobs of many tasks b…
Polynomial based methods have recently been used in several works for mitigating the effect of stragglers (slow or failed nodes) in distributed matrix computations. For a system with $n$ worker nodes where $s$ can be stragglers, these approaches allow for an optimal recovery threshold, whereby the intended result can be decoded as long as any $(n-s)$ worker nodes complete their tasks. However, they suffer from serious numerical issues owing to the condition number of the corresponding real Vandermonde-structured recovery matrices; this condition number grows exponentially in $n$. We present a …
University of Maryland（马里兰大学）；Imperial College London（帝国理工学院）
In distributed synchronous gradient descent (GD) the main performance bottleneck for the per-iteration completion time is the slowest \textit{straggling} workers. To speed up GD iterations in the presence of stragglers, coded distributed computation techniques are implemented by assigning redundant computations to workers. In this paper, we propose a novel gradient coding (GC) scheme that utilizes dynamic clustering, denoted by GC-DC, to speed up the gradient calculation. Under time-correlated straggling behavior, GC-DC aims at regulating the number of straggling workers in each cluster based …
In large-scale distributed computing clusters, such as Amazon EC2, there are several types of "system noise" that can result in major degradation of performance: bottlenecks due to limited communication bandwidth, latency due to straggler nodes, etc. On the other hand, these systems enjoy abundance of redundancy - a vast number of computing nodes and large storage capacity. There have been recent results that demonstrate the impact of coding for efficient utilization of computation and storage redundancy to alleviate the effect of stragglers and communication bottlenecks in homogeneous cluster…
Simula UiB（卑尔根西穆拉研究中心）；Chalmers University of Technology（查尔姆斯理工大学）
We present a novel coded federated learning (FL) scheme for linear regression that mitigates the effect of straggling devices while retaining the privacy level of conventional FL. The proposed scheme combines one-time padding to preserve privacy and gradient codes to yield resiliency against stragglers and consists of two phases. In the first phase, the devices share a one-time padded version of their local data with a subset of other devices. In the second phase, the devices and the central server collaboratively and iteratively train a global linear model using gradient codes on the one-time…
Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Tsinghua University（清华大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Imperial College London（伦敦帝国理工学院）
Distributed computing enables large-scale computation tasks to be processed over multiple workers in parallel. However, the randomness of communication and computation delays across workers causes the straggler effect, which may degrade the performance. Coded computation helps to mitigate the straggler effect, but the amount of redundant load and their assignment to the workers should be carefully optimized. In this work, we consider a multi-master heterogeneous-worker distributed computing scenario, where multiple matrix multiplication tasks are encoded and allocated to workers for parallel c…
The emerging large-scale and data-hungry algorithms require the computations to be delegated from a central server to several worker nodes. One major challenge in the distributed computations is to tackle delays and failures caused by the stragglers. To address this challenge, introducing efficient amount of redundant computations via distributed coded computation has received significant attention. Recent approaches in this area have mainly focused on introducing minimum computational redundancies to tolerate certain number of stragglers. To the best of our knowledge, the current literature l…
We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which is due to the unpredictable latency in waiting for slowest nodes (or stragglers) to finish their tasks. We propose a novel coding strategy, named \emph{entangled polynomial code}, for designing the intermediate computations at the worker nodes in order to minimize the recovery threshold (i.e., the number of workers that we need to wait for in order to compu…
Coded distributed computing was recently introduced to mitigate the effect of stragglers on distributed computing. This paper combines ideas of approximate computing with coded computing to further accelerate computation. We propose successive approximation coding (SAC) techniques that realize a tradeoff between accuracy and speed, allowing the distributed computing system to produce approximations that increase in accuracy over time. If a sufficient number of compute nodes finish their tasks, SAC exactly recovers the desired computation. We theoretically provide design guidelines for our SAC …
We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1) We construct new codes for matrix multiplication that achieve the same fault/straggler tolerance as the previously constructed MatDot Codes and Polynomial Codes. Unlike previous codes that use polynomials expanded in a monomial basis, our codes uses a basis of orthogonal polynomials. 2) We show that the condition number of every $m \times m$ sub-matrix of an …
Coded distributed computing framework enables large-scale machine learning (ML) models to be trained efficiently in a distributed manner, while mitigating the straggler effect. In this work, we consider a multi-task assignment problem in a coded distributed computing system, where multiple masters, each with a different matrix multiplication task, assign computation tasks to workers with heterogeneous computing capabilities. Both dedicated and probabilistic worker assignment models are considered, with the objective of minimizing the average completion time of all computations. For dedicated w…
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular workaround to the well known ``straggling nodes'' problem, in particular, by matching linear coding for linear computation tasks. It was observed that decoding tends to amplify the computation ``noise'', i.e., the numerical errors at the computation nodes. We propose taking advantage of the case that more nodes return than minimally required. We show how a cleve…
Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple solution of replicating computation entails significant resource overhead. Coded computation has emerged as a resource-efficient alternative, wherein multiple units of data are encoded to create parity units and the function to be computed is applied to each of these units on distinct servers. A decoder can use the available function outputs to decode the unavailab…
