Straggler-aware Distributed Learning: Communication Computation Latency Trade-off
Imperial College London（帝国理工学院）；University of Maryland（马里兰大学）
Emre Ozfatura, Sennur Ulukus, Deniz Gunduz
备注：
This paper was presented in part at the 2019 IEEE International Symposium on Information Theory (ISIT) in Paris, France, and at the 2019 IEEE Data Science Workshop in Minneapolis, USA
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-utilization due to treating workers as straggler/non-straggler and discarding partial computations carried out by stragglers. In this paper, to overcome these drawbacks, we consider multi-message communication (MMC) by allowing multiple computations to be conveyed from each worker per iteration, and design straggler avoidance techniques accordingly. Then, we analyze how the proposed designs can be employed efficiently to seek a balance between the computation and communication latency to minimize the overall latency. Furthermore, through extensive simulations, both model-based and real implementation on Amazon EC2 servers, we identify the advantages and disadvantages of these designs in different settings, and demonstrate that MMC can help improve upon existing straggler avoidance schemes.
Dealing with the shear size and complexity of today's massive data sets requires computational platforms that can analyze data in a parallelized and distributed fashion. A major bottleneck that arises in such modern distributed computing environments is that some of the worker nodes may run slow. These nodes a.k.a.~stragglers can significantly slow down computation as the slowest node may dictate the overall computational time. A recent computational framework, called encoded optimization, creates redundancy in the data to mitigate the effect of stragglers. In this paper we develop novel mathe…
Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in waiting for the slowest learners (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect convergence. In this work we present a novel theoretical characterization of the speed-up offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime (wallclock time). The novelty in our work is that our runtime analysis considers random straggler delays, which helps us design …
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…
Redundancy for straggler mitigation, originally in data download and more recently in distributed computing context, has been shown to be effective both in theory and practice. Analysis of systems with redundancy has drawn significant attention and numerous papers have studied pain and gain of redundancy under various service models and assumptions on the straggler characteristics. We here present a cost (pain) vs. latency (gain) analysis of using simple replication or erasure coding for straggler mitigation in executing jobs with many tasks. We quantify the effect of the tail of task executio…
Redundancy for straggler mitigation, originally in data download and more recently in distributed computing context, has been shown to be effective both in theory and practice. Analysis of systems with redundancy has drawn significant attention and numerous papers have studied pain and gain of redundancy under various service models and assumptions on the straggler characteristics. We here present a cost (pain) vs. latency (gain) analysis of using simple replication or erasure coding for straggler mitigation in executing jobs with many tasks. We quantify the effect of the tail of task executio…
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…
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…
Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in runtime as it waits for the slowest workers (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect the convergence error. In this work, we present a novel theoretical characterization of the speedup offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime(wallclock time). The main novelty in our work is that our runtime analysis considers random straggling dela…
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…
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…
We study the expected completion time of some recently proposed algorithms for distributed computing which redundantly assign computing tasks to multiple machines in order to tolerate a certain number of machine failures. We analytically show that not only the amount of redundancy but also the task-to-machine assignments affect the latency in a distributed system. We study systems with a fixed number of computing tasks that are split in possibly overlapping batches, and independent exponentially distributed machine service times. We show that, for such systems, the uniform replication of non- …
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 …
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…
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…
In distributed computing systems with stragglers, various forms of redundancy can improve the average delay performance. We study the optimal replication of data in systems where the job execution time is a stochastically decreasing and convex random variable. We show that in such systems, the optimum assignment policy is the balanced replication of disjoint batches of data. Furthermore, for Exponential and Shifted-Exponential service times, we derive the optimum redundancy levels for minimizing both expected value and the variance of the job completion time. Our analysis shows that, the optim…
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)^…
We propose a novel distributed iterative linear inverse solver method. Our method, PolyLin, has significantly lower communication cost, both in terms of number of rounds as well as number of bits, in comparison with the state of the art at the cost of higher computational complexity and storage. Our algorithm also has a built-in resilience to straggling and faulty computation nodes. We develop a natural variant of our main algorithm that trades off communication cost for computational complexity. Our method is inspired by ideas in error correcting codes.
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…
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…
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…
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）
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…
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…
Master-worker distributed computing systems use task replication in order to mitigate the effect of slow workers, known as stragglers. Tasks are grouped into batches and assigned to one or more workers for execution. We first consider the case when the batches do not overlap and, using the results from majorization theory, show that, for a general class of workers' service time distributions, a balanced assignment of batches to workers minimizes the average job compute time. We next show that this balanced assignment of non-overlapping batches achieves lower average job compute time compared t…
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…
In this paper, we study the problem of latency and reliability trade-off in ultra-reliable low-latency communication (URLLC) in the presence of decoding complexity constraints. We consider linear block encoded codewords transmitted over a binary-input AWGN channel and decoded with order-statistic (OS) decoder. We first investigate the performance of OS decoders as a function of decoding complexity and propose an empirical model that accurately quantifies the corresponding trade-off. Next, a consistent way to compute the aggregate latency for complexity constrained receivers is presented, where…
We consider a mobile edge computing scenario where a number of devices want to perform a linear inference $\boldsymbol{W}\boldsymbol{x}$ on some local data $\boldsymbol{x}$ given a network-side matrix $\boldsymbol{W}$. The computation is performed at the network edge over a number of edge servers. We propose a coding scheme that provides information-theoretic privacy against $z$ colluding (honest-but-curious) edge servers, while minimizing the overall latency\textemdash comprising upload, computation, download, and decoding latency\textemdash in the presence of straggling servers. The proposed…
High-fidelity, real-time interactive applications are envisioned with the emergence of the Internet of Things (IoT) and tactile Internet by means of ultra-reliable low-latency communications (URLLC). Exploiting time diversity for fulfilling the URLLC requirements in an energy efficient manner is a challenging task due to the nontrivial interplay among packet size, retransmission rounds and delay, and transmit power. In this paper, we study the fundamental energy-latency tradeoff in URLLC systems employing incremental redundancy (IR) hybrid automatic repeat request (HARQ). We cast the average e…
A novel fault-tolerant computation technique based on array Belief Propagation (BP)-decodable XOR (BP-XOR) codes is proposed for distributed matrix-matrix multiplication. The proposed scheme is shown to be configurable and suited for modern hierarchical compute architectures such as Graphical Processing Units (GPUs) equipped with multiple nodes, whereby each has many small independent processing units with increased core-to-core communications. The proposed scheme is shown to outperform a few of the well--known earlier strategies in terms of total end-to-end execution time while in presence of…
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 …
A Fog Radio Access Network (F-RAN) is a cellular wireless system that enables content delivery via the caching of popular content at edge nodes (ENs) and cloud processing. The existing information-theoretic analyses of F-RAN systems, and special cases thereof, make the assumption that all requests should be guaranteed the same delivery latency, which results in identical latency for all files in the content library. In practice, however, contents may have heterogeneous timeliness requirements depending on the applications that operate on them. Given per-EN cache capacity constraint, there exis…
We propose a unified coded framework for distributed computing with straggling servers, by introducing a tradeoff between "latency of computation" and "load of communication" for some linear computation tasks. We show that the coded scheme of [1]-[3] that repeats the intermediate computations to create coded multicasting opportunities to reduce communication load, and the coded scheme of [4], [5] that generates redundant intermediate computations to combat against straggling servers can be viewed as special instances of the proposed framework, by considering two extremes of this tradeoff: mini…
The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two dif…
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…
A fog radio access network (F-RAN) is studied, in which $K_T$ edge nodes (ENs) connected to a cloud server via orthogonal fronthaul links, serve $K_R$ users through a wireless Gaussian interference channel. Both the ENs and the users have finite-capacity cache memories, which are filled before the user demands are revealed. While a centralized placement phase is used for the ENs, which model static base stations, a decentralized placement is leveraged for the mobile users. An achievable transmission scheme is presented, which employs a combination of interference alignment, zero-forcing and in…
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…
In the Cloud Radio Access Network (C-RAN) architecture, the baseband signals from multiple remote radio heads are processed in a centralized baseband unit (BBU) pool. This architecture allows network operators to adapt the BBU's computational resources to the aggregate access load experienced at the BBU, which can change in every air-interface access frame. The degree of savings that can be achieved by adapting the resources is a tradeoff between savings, adaptation frequency, and increased queuing time. If the time scale for adaptation of the resource multiplexing is greater than the access f…
This paper studies the decentralized coded caching for a Fog Radio Access Network (F-RAN), whereby two edge-nodes (ENs) connected to a cloud server via fronthaul links with limited capacity are serving the requests of $K_r$ users. We consider all ENs and users are equipped with caches. A decentralized content placement is proposed to independently store contents at each network node during the off-peak hours. After that, we design a coded delivery scheme in order to deliver the user demands during the peak-hours under the objective of minimizing the normalized delivery time (NDT), which refers…
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…
Beijing University of Posts and Telecommunications（北京邮电大学）
In this letter, we study a wireless federated learning (FL) system where network pruning is applied to local users with limited resources. Although pruning is beneficial to reduce FL latency, it also deteriorates learning performance due to the information loss. Thus, a trade-off problem between communication and learning is raised. To address this challenge, we quantify the effects of network pruning and packet error on the learning performance by deriving the convergence rate of FL with a non-convex loss function. Then, closed-form solutions for pruning control and bandwidth allocation are p…
With the phenomenal growth of the Internet of Things (IoT), Ultra Reliable Low Latency Communications (URLLC) has potentially been the enabler to guarantee the stringent requirements on latency and reliability. However, how to achieve low latency and ultra-reliability with the random arrival remains open. In this paper, a queue-aware variable-length channel coding is presented over the single URLLC user link, in which the finite blocklength of channel coding is determined based on the random arrival. More particularly, a cross-layer approach is proposed for the URLLC user to establish the opti…
A fog-aided wireless network architecture is studied in which edge-nodes (ENs), such as base stations, are connected to a cloud processor via dedicated fronthaul links, while also being endowed with caches. Cloud processing enables the centralized implementation of cooperative transmission strategies at the ENs, albeit at the cost of an increased latency due to fronthaul transfer. In contrast, the proactive caching of popular content at the ENs allows for the low-latency delivery of the cached files, but with generally limited opportunities for cooperative transmission among the ENs. The inter…
