Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A significant performance bottleneck for the per-iteration completion time in distributed synchronous GD is $straggling$ workers. Coded distributed computation techniques have been introduced recently to mitigate stragglers and to speed up GD iterations by assigning redundant computations to workers. In this paper, we consider gradient coding (GC), and propose a novel dynamic GC scheme, which assigns redundant data to workers to acquire the flexibility to dynamically choose from among a set of possible codes depending on the past straggling behavior. In particular, we consider GC with clustering, and regulate the number of stragglers in each cluster by dynamically forming the clusters at each iteration; hence, the proposed scheme is called $GC$ $with$ $dynamic$ $clustering$ (GC-DC). Under a time-correlated straggling behavior, GC-DC gains from adapting to the straggling behavior over time such that, at each iteration, GC-DC aims at distributing the stragglers across clusters as uniformly as possible based on the past straggler behavior. For both homogeneous and heterogeneous worker models, we numerically show that GC-DC provides significant improvements in the average per-iteration completion time without an increase in the communication load compared to the original GC scheme.
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 …
Wall-clock convergence time and communication load are key performance metrics for the distributed implementation of stochastic gradient descent (SGD) in parameter server settings. Communication-adaptive distributed Adam (CADA) has been recently proposed as a way to reduce communication load via the adaptive selection of workers. CADA is subject to performance degradation in terms of wall-clock convergence time in the presence of stragglers. This paper proposes a novel scheme named grouping-based CADA (G-CADA) that retains the advantages of CADA in reducing the communication load, while increa…
We propose a novel coding theoretic framework for mitigating stragglers in distributed learning. We show how carefully replicating data blocks and coding across gradients can provide tolerance to failures and stragglers for Synchronous Gradient Descent. We implement our schemes in python (using MPI) to run on Amazon EC2, and show how we compare against baseline approaches in running time and generalization error.
Gradient descent and its many variants, including mini-batch stochastic gradient descent, form the algorithmic foundation of modern large-scale machine learning. Due to the size and scale of modern data, gradient computations are often distributed across multiple compute nodes. Unfortunately, such distributed implementations can face significant delays caused by straggler nodes, i.e., nodes that are much slower than average. Gradient coding is a new technique for mitigating the effect of stragglers via algorithmic redundancy. While effective, previously proposed gradient codes can be computati…
Approximate Gradient Coding for Distributed Learning with Heterogeneous Stragglers
Korea Advanced Institute of Science and Technology School of Electrical Engineering（韩国科学技术院电子工程学院）；Seoul National University Department of Electrical and Computer Engineering（首尔国立大学电气与计算机工程学院）
Slow running or straggler tasks can significantly reduce computation speed in distributed computation. Recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in certain linear computational steps of the optimization algorithm, thus completing the computation without waiting for the stragglers. In this paper, we propose an alternate approach where we embed the redundancy directly in the data itself, and allow the computation to proceed completely oblivious to encoding. We propose several encoding schemes, and demonstrate …
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon E…
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…
Imperial College London（帝国理工学院）；University of Maryland（马里兰大学）
When gradient descent (GD) is scaled to many parallel workers for large scale machine learning problems, its per-iteration computation time is limited by the straggling workers. Straggling workers can be tolerated by assigning redundant computations and coding across data and computations, but in most existing schemes, each non-straggling worker transmits one message per iteration to the parameter server (PS) after completing all its computations. Imposing such a limitation results in two main drawbacks; over-computation due to inaccurate prediction of the straggling behaviour, and under-utili…
Imperial College London（帝国理工学院）；University of Maryland, College Park（马里兰大学帕克分校）
Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing servers (i.e., workers) to speed up GD iterations. While distributed computing can increase the computation speed significantly, the per-iteration completion time is limited by the slowest straggling workers. Coded distributed computing can mitigate straggling workers by introducing redundant computations; however, existing coded computing schemes are mainly d…
Gradient-based distributed learning in Parameter Server (PS) computing architectures is subject to random delays due to straggling worker nodes, as well as to possible communication bottlenecks between PS and workers. Solutions have been recently proposed to separately address these impairments based on the ideas of gradient coding, worker grouping, and adaptive worker selection. This paper provides a unified analysis of these techniques in terms of wall-clock time, communication, and computation complexity measures. Furthermore, in order to combine the benefits of gradient coding and grouping…
Distributed implementations of gradient-based methods, wherein a server distributes gradient computations across worker machines, need to overcome two limitations: delays caused by slow running machines called 'stragglers', and communication overheads. Recently, Ye and Abbe [ICML 2018] proposed a coding-theoretic paradigm to characterize a fundamental trade-off between computation load per worker, communication overhead per worker, and straggler tolerance. However, their proposed coding schemes suffer from heavy decoding complexity and poor numerical stability. In this paper, we develop a comm…
Distributed implementations of gradient-based methods, wherein a server distributes gradient computations across worker machines, suffer from slow running machines, called 'stragglers'. Gradient coding is a coding-theoretic framework to mitigate stragglers by enabling the server to recover the gradient sum in the presence of stragglers. 'Approximate gradient codes' are variants of gradient codes that reduce computation and storage overhead per worker by allowing the server to approximately reconstruct the gradient sum. In this work, our goal is to construct approximate gradient codes that are …
University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）；University of Southern California（南加利福尼亚大学）
We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key system bottlenecks: communication bandwidth and stragglers' delays. In particular, Ring-AllReduce (RAR) design has been proposed to avoid bandwidth bottleneck at any particular node by allowing each worker to only communicate with its neighbors that are arranged in a logical ring. On the other hand, Gradient Coding (GC) has been recently proposed to mitigate str…
We consider distributed gradient descent in the presence of stragglers. Recent work on \em gradient coding \em and \em approximate gradient coding \em have shown how to add redundancy in distributed gradient descent to guarantee convergence even if some workers are \em stragglers\em---that is, slow or non-responsive. In this work we propose an approximate gradient coding scheme called \em Stochastic Gradient Coding \em (SGC), which works when the stragglers are random. SGC distributes data points redundantly to workers according to a pair-wise balanced design, and then simply ignores the strag…
This paper focuses on mitigating the impact of stragglers in distributed learning system. Unlike the existing results designed for a fixed number of stragglers, we developed a new scheme called Adaptive Gradient Coding(AGC) with flexible tolerance of various number of stragglers. Our scheme gives an optimal tradeoff between computation load, straggler tolerance and communication cost. In particular, it allows to minimize the communication cost according to the real-time number of stragglers in the practical environments. Implementations on Amazon EC2 clusters using Python with mpi4py package v…
Gradient descent algorithms are widely used in machine learning. In order to deal with huge volume of data, we consider the implementation of gradient descent algorithms in a distributed computing setting where multiple workers compute the gradient over some partial data and the master node aggregates their results to obtain the gradient over the whole data. However, its performance can be severely affected by straggler workers. Recently, some coding-based approaches are introduced to mitigate the straggler problem, but they are efficient only when the workers are homogeneous, i.e., having the…
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…
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…
In distributed machine learning (DML), the training data is distributed across multiple worker nodes to perform the underlying training in parallel. One major problem affecting the performance of DML algorithms is presence of stragglers. These are nodes that are terribly slow in performing their task which results in under-utilization of the training data that is stored in them. Towards this, gradient coding mitigates the impact of stragglers by adding sufficient redundancy in the data. Gradient coding and other straggler mitigation schemes assume that the straggler behavior of the worker node…
Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic redundancy. Prior work in coded computation and gradient coding has mainly focused on exact recovery of the desired output. However, slightly inexact solutions can be acceptable in applications that are robust to noise, such as model training via gradient-based algorithms. In this work, we present computationally simple gradient codes based on sparse graphs t…
The Graduate Center, CUNY（纽约市立大学研究生中心）；Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院）；CUNY Queens College & Graduate Center（纽约市立大学皇后学院及研究生中心）
Coded distributed computation has become common practice for performing gradient descent on large datasets to mitigate stragglers and other faults. This paper proposes a novel algorithm that encodes the partial derivatives themselves and furthermore optimizes the codes by performing lossy compression on the derivative codewords by maximizing the information contained in the codewords while minimizing the information between the codewords. The utility of this application of coding theory is a geometrical consequence of the observed fact in optimization research that noise is tolerable, sometime…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which concerns coding schemes where the replication factor of the data is too low to recover the full gradient exactly. Our work is motivated by the challenge of creating approximate gradient coding schemes that simultaneously work well in both the adversarial and stochastic models. To that end, we introduce novel approximate gradient codes based on expander graphs, in …
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…
Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has demonstrated that straggler mitigation can be viewed as a problem of designing erasure codes. For matrices $\mathbf A$ and $\mathbf B$, the technique essentially maps the computation of $\mathbf A^T \mathbf B$ into the multiplication of smaller (coded) submatrices. The stragglers are treated as erasures in this process. The computation can be completed as long as a cer…
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…
We consider distributed learning in the presence of slow and unresponsive worker nodes, referred to as stragglers. In order to mitigate the effect of stragglers, gradient coding redundantly assigns partial computations to the worker such that the overall result can be recovered from only the non-straggling workers. Gradient codes are designed to tolerate a fixed number of stragglers. Since the number of stragglers in practice is random and unknown a priori, tolerating a fixed number of stragglers can yield a sub-optimal computation load and can result in higher latency. We propose a gradient c…
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 o…
In a distributed computing system operating according to the map-shuffle-reduce framework, coding data prior to storage can be useful both to reduce the latency caused by straggling servers and to decrease the inter-server communication load in the shuffling phase. In prior work, a concatenated coding scheme was proposed for a matrix multiplication task. In this scheme, the outer Maximum Distance Separable (MDS) code is leveraged to correct erasures caused by stragglers, while the inner repetition code is used to improve the communication efficiency in the shuffling phase by means of coded mul…
Gradient coding allows a master node to derive the aggregate of the partial gradients, calculated by some worker nodes over the local data sets, with minimum communication cost, and in the presence of stragglers. In this paper, for gradient coding with linear encoding, we characterize the optimum communication cost for heterogeneous distributed systems with \emph{arbitrary} data placement, with $s \in \mathbb{N}$ stragglers and $a \in \mathbb{N}$ adversarial nodes. In particular, we show that the optimum communication cost, normalized by the size of the gradient vectors, is equal to $(r-s-2a)^…
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 …
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…
Existing gradient coding schemes introduce identical redundancy across the coordinates of gradients and hence cannot fully utilize the computation results from partial stragglers. This motivates the introduction of diverse redundancies across the coordinates of gradients. This paper considers a distributed computation system consisting of one master and $N$ workers characterized by a general partial straggler model and focuses on solving a general large-scale machine learning problem with $L$ model parameters. We show that it is sufficient to provide at most $N$ levels of redundancies for tole…
An adaptive delay-tolerant distributed space-time coding (DSTC) scheme that exploits feedback is proposed for two-hop cooperative MIMO networks. Maximum likelihood (ML) receivers and adjustable code matrices are considered subject to a power constraint with a decode-and-forward (DF) cooperation strategy. In the proposed delay-tolerant DSTC scheme, an adjustable code matrix is employed to transform the space-time coded matrix at the relay nodes. Least-squares (LS) algorithms are developed with reduced computational complexity to adjust the parameters of the codes. Simulation results show that t…
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for computation at the agents is affected by the availability of local resources giving rise to the "straggler problem" in which the computation results are held back by unresponsive agents. For this problem, linear coding of the matrix sub-blocks can be used to introduce resilience toward straggling. The Parameter Server (PS) utilizes a channel code and distributes the matrices to the workers for multiplication. It then produces an approxim…
Distributed matrix computations -- matrix-matrix or matrix-vector multiplications -- are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in terms of its straggler resilience, or (ii) suffers from numerical problems, i.e., there is a blow-up of round-off errors in the decoded result owing to the high condition numbers of the corresponding decoding matrices. Our work presents convolutional coding approach to this problem that removes these limitations. It is optimal in terms of its straggler resilie…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing solutions, both in the applicable range of parameters and in the complexity of the involved algorithms. Second, we introduce an approximate variant of the gradient coding problem, in which we settle for approximate gradient computation instead of the exact one. This approach enables graceful degradation, i.e., the $\ell_2$ error of the approximate gradient is a decr…
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 …
Inexpensive cloud services, such as serverless computing, are often vulnerable to straggling nodes that increase end-to-end latency for distributed computation. We propose and implement simple yet principled approaches for straggler mitigation in serverless systems for matrix multiplication and evaluate them on several common applications from machine learning and high-performance computing. The proposed schemes are inspired by error-correcting codes and employ parallel encoding and decoding over the data stored in the cloud using serverless workers. This creates a fully distributed computing …
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…
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 …
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for the computations at the agents is affected by the availability of local resources and/or poor channel conditions giving rise to the "straggler problem". As a remedy to this problem, we employ Unequal Error Protection (UEP) codes to obtain an approximation of the matrix product in the distributed computation setting to provide higher protection for the blocks with higher effect on the final result. We characterize the performance of the p…
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 …
Coding schemes are presented that provide the ability to correct and detect computational errors while using dot-product engines for integer vector--matrix multiplication. Both the $L_1$-metric and the Hamming metric are considered.
Coded computing is an effective technique to mitigate "stragglers" in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown to be effective in straggler mitigation by making the computation time depend only on the fastest workers. However, these schemes completely ignore the work done by the straggling workers resulting in a waste of computational resources. To reduce the amount of work left unfinished at workers, one can further decompose the matrix multiplication task into smaller sub-tasks, and assign multiple sub-tasks to each worker,…
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…
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…
A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. \textit{Leverage score sampling} provides a compressed approximation of a data matrix using an importance weighted subset. \textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient using multiple unreliable worker nodes. By designing coding matrices, gradient coded computations can be made resilient to stragglers, which are nodes in a distributed network that degrade syst…
