Age-Based Coded Computation for Bias Reduction in Distributed Learning

Coded computation can be used to speed up distributed learning in the presence of straggling workers. Partial recovery of the gradient vector can further reduce the computation time at each iteration; however, this can result in biased estimators, which may slow down convergence, or even cause divergence. Estimator bias will be particularly prevalent when the straggling behavior is correlated over time, which results in the gradient estimators being dominated by a few fast servers. To mitigate biased estimators, we design a $timely$ dynamic encoding framework for partial recovery that includes an ordering operator that changes the codewords and computation orders at workers over time. To regulate the recovery frequencies, we adopt an $age$ metric in the design of the dynamic encoding scheme. We show through numerical results that the proposed dynamic encoding strategy increases the timeliness of the recovered computations, which as a result, reduces the bias in model updates, and accelerates the convergence compared to the conventional static partial recovery schemes

Coded Distributed Computing with Partial Recovery

Coded computation techniques provide robustness against straggling workers in distributed computing. However, most of the existing schemes require exact provisioning of the straggling behaviour and ignore the computations carried out by straggling workers. Moreover, these schemes are typically designed to recover the desired computation results accurately, while in many machine learning and iterative optimization algorithms, faster approximate solutions are known to result in an improvement in the overall convergence time. In this paper, we first introduce a novel coded matrix-vector multiplication scheme, called coded computation with partial recovery (CCPR), which benefits from the advantages of both coded and uncoded computation schemes, and reduces both the computation time and the decoding complexity by allowing a trade-off between the accuracy and the speed of computation. We then extend this approach to distributed implementation of more general computation tasks by proposing a coded communication scheme with partial recovery, where the results of subtasks computed by the workers are coded before being communicated. Numerical simulations on a large linear regression task confirm the benefits of the proposed distributed computation scheme with partial recovery in terms of the trade-off between the computation accuracy and latency.Comment: Accepted to IEEE Transactions on Information Theory. Presented in part at the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing in Brighton, U

On Gradient Coding with Partial Recovery

We consider a generalization of the recently proposed gradient coding framework where a large dataset is divided across $n$ workers and each worker transmits to a master node one or more linear combinations of the gradients over the data subsets assigned to it. Unlike the conventional framework which requires the master node to recover the sum of the gradients over all the data subsets in the presence of $s$ straggler workers, we relax the goal of the master node to computing the sum of at least some $\alpha$ fraction of the gradients. The broad goal of our work is to study the optimal computation and communication load per worker for this approximate gradient coding framework. We begin by deriving a lower bound on the computation load of any feasible scheme and also propose a strategy which achieves this lower bound, albeit at the cost of high communication load and a number of data partitions which can be polynomial in the number of workers $n$. We then restrict attention to schemes which utilize a number of data partitions equal to $n$ and propose schemes based on cyclic assignment which have a lower communication load. When each worker transmits a single linear combination, we also prove lower bounds on the computation load of any scheme using $n$ data partitions

Efficient Replication for Straggler Mitigation in Distributed Computing

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 to the overlapping schemes proposed in the literature. Furthermore, we derive the optimum redundancy level as a function of the service time distribution at workers. We show that the redundancy level that minimizes average job compute time is not necessarily the same as the redundancy level that maximizes the predictability of job compute time, and thus there exists a trade-off between optimizing the two metrics. Finally, by running experiments on Google cluster traces, we observe that redundancy can reduce the compute time of the jobs in Google clusters by an order of magnitude, and that the optimum level of redundancy depends on the distribution of tasks' service time

Approximate Gradient Coding with Optimal Decoding

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 which each machine receives exactly two blocks of data points. We analyze the decoding error both in the random and adversarial straggler setting, when optimal decoding coefficients are used. We show that in the random setting, our schemes achieve an error to the gradient that decays exponentially in the replication factor. In the adversarial setting, the error is nearly a factor of two smaller than any existing code with similar performance in the random setting. We show convergence bounds both in the random and adversarial setting for gradient descent under standard assumptions using our codes. In the random setting, our convergence rate improves upon block-box bounds. In the adversarial setting, we show that gradient descent can converge down to a noise floor that scales linearly with the adversarial error to the gradient. We demonstrate empirically that our schemes achieve near-optimal error in the random setting and converge faster than algorithms which do not use the optimal decoding coefficients

Slow and Stale Gradients Can Win the Race

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 delays, which helps us design and compare distributed SGD algorithms that strike a balance between straggling and staleness. We also provide a new error convergence analysis of asynchronous SGD variants without bounded or exponential delay assumptions. Finally, based on our theoretical characterization of the error-runtime trade-off, we propose a method of gradually varying synchronicity in distributed SGD and demonstrate its performance on CIFAR10 dataset.Comment: Some of the results have appeared in AISTATS 2018. This is an extended version with additional results, in particular, an adaptive synchronicity strategy called AdaSync. arXiv admin note: substantial text overlap with arXiv:1803.0111

A Survey of Coded Distributed Computing

Distributed computing has become a common approach for large-scale computation of tasks due to benefits such as high reliability, scalability, computation speed, and costeffectiveness. However, distributed computing faces critical issues related to communication load and straggler effects. In particular, computing nodes need to exchange intermediate results with each other in order to calculate the final result, and this significantly increases communication overheads. Furthermore, a distributed computing network may include straggling nodes that run intermittently slower. This results in a longer overall time needed to execute the computation tasks, thereby limiting the performance of distributed computing. To address these issues, coded distributed computing (CDC), i.e., a combination of coding theoretic techniques and distributed computing, has been recently proposed as a promising solution. Coding theoretic techniques have proved effective in WiFi and cellular systems to deal with channel noise. Therefore, CDC may significantly reduce communication load, alleviate the effects of stragglers, provide fault-tolerance, privacy and security. In this survey, we first introduce the fundamentals of CDC, followed by basic CDC schemes. Then, we review and analyze a number of CDC approaches proposed to reduce the communication costs, mitigate the straggler effects, and guarantee privacy and security. Furthermore, we present and discuss applications of CDC in modern computer networks. Finally, we highlight important challenges and promising research directions related to CD

Communication-Efficient Edge AI: Algorithms and Systems

Artificial intelligence (AI) has achieved remarkable breakthroughs in a wide range of fields, ranging from speech processing, image classification to drug discovery. This is driven by the explosive growth of data, advances in machine learning (especially deep learning), and easy access to vastly powerful computing resources. Particularly, the wide scale deployment of edge devices (e.g., IoT devices) generates an unprecedented scale of data, which provides the opportunity to derive accurate models and develop various intelligent applications at the network edge. However, such enormous data cannot all be sent from end devices to the cloud for processing, due to the varying channel quality, traffic congestion and/or privacy concerns. By pushing inference and training processes of AI models to edge nodes, edge AI has emerged as a promising alternative. AI at the edge requires close cooperation among edge devices, such as smart phones and smart vehicles, and edge servers at the wireless access points and base stations, which however result in heavy communication overheads. In this paper, we present a comprehensive survey of the recent developments in various techniques for overcoming these communication challenges. Specifically, we first identify key communication challenges in edge AI systems. We then introduce communication-efficient techniques, from both algorithmic and system perspectives for training and inference tasks at the network edge. Potential future research directions are also highlighted.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl