arXiv subjects

Gauri Joshi

Publications and source records attributed to Gauri Joshi.

89 records · Page 5Linked to original sources

arXiv2019

Accelerating Deep Learning by Focusing on the Biggest Losers

This paper introduces Selective-Backprop, a technique that accelerates the training of deep neural networks (DNNs) by prioritizing examples with high loss at each iteration. Selective-Backprop uses the output of a training example's forward pass to decide whether to use that example to compute gradients and update parameters, or to skip immediately to the next example. By reducing the number of computationally-expensive backpropagation steps performed, Selective-Backprop accelerates training. Evaluation on CIFAR10, CIFAR100, and SVHN, across a variety of modern image models, shows that Selective-Backprop converges to target error rates up to 3.5x faster than with standard SGD and between 1.02--1.8x faster than a state-of-the-art importance sampling approach. Further acceleration of 26% can be achieved by using stale forward pass results for selection, thus also skipping forward passes of low priority examples.

cs.LG↗

arXiv2019

Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGD

Large-scale machine learning training, in particular distributed stochastic gradient descent, needs to be robust to inherent system variability such as node straggling and random communication delays. This work considers a distributed training framework where each worker node is allowed to perform local model updates and the resulting models are averaged periodically. We analyze the true speed of error convergence with respect to wall-clock time (instead of the number of iterations), and analyze how it is affected by the frequency of averaging. The main contribution is the design of AdaComm, an adaptive communication strategy that starts with infrequent averaging to save communication delay and improve convergence speed, and then increases the communication frequency in order to achieve a low error floor. Rigorous experiments on training deep neural networks show that AdaComm can take $3 \times$ less time than fully synchronous SGD, and still reach the same final training loss.

cs.LG↗

arXiv2019

Correlated Multi-armed Bandits with a Latent Random Source

We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a generalized upper-confidence-bound (UCB) algorithm that identifies certain arms as $non-competitive$, and avoids exploring them. As a result, we reduce a $K$-armed bandit problem to a $C+1$-armed problem, where $C+1$ includes the best arm and $C$ $competitive$ arms. Our regret analysis shows that the competitive arms need to be pulled $\mathcal{O}(\log T)$ times, while the non-competitive arms are pulled only $\mathcal{O}(1)$ times. As a result, there are regimes where our algorithm achieves a $\mathcal{O}(1)$ regret as opposed to the typical logarithmic regret scaling of multi-armed bandit algorithms. We also evaluate lower bounds on the expected regret and prove that our correlated-UCB algorithm achieves $\mathcal{O}(1)$ regret whenever possible.

stat.ML↗

arXiv2019

Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms

Communication-efficient SGD algorithms, which allow nodes to perform local updates and periodically synchronize local models, are highly effective in improving the speed and scalability of distributed SGD. However, a rigorous convergence analysis and comparative study of different communication-reduction strategies remains a largely open problem. This paper presents a unified framework called Cooperative SGD that subsumes existing communication-efficient SGD algorithms such as periodic-averaging, elastic-averaging and decentralized SGD. By analyzing Cooperative SGD, we provide novel convergence guarantees for existing algorithms. Moreover, this framework enables us to design new communication-efficient SGD algorithms that strike the best balance between reducing communication overhead and achieving fast error convergence with low error floor.

cs.LG↗

arXiv2019

Service Rate Region of Content Access from Erasure Coded Storage

We consider storage systems in which $K$ files are stored over $N$ nodes. A node may be systematic for a particular file in the sense that access to it gives access to the file. Alternatively, a node may be coded, meaning that it gives access to a particular file only when combined with other nodes (which may be coded or systematic). Requests for file $f_k$ arrive at rate $λ_k$, and we are interested in the rate that can be served by a particular system. In this paper, we determine the set of request arrival rates for the a $3$-file coded storage system. We also provide an algorithm to maximize the rate of requests served for file $K$ given $λ_1,\dots, λ_{K-1}$ in a general $K$-file case.

cs.IT↗

arXiv2018

Active Distribution Learning from Indirect Samples

This paper studies the problem of {\em learning} the probability distribution $P_X$ of a discrete random variable $X$ using indirect and sequential samples. At each time step, we choose one of the possible $K$ functions, $g_1, \ldots, g_K$ and observe the corresponding sample $g_i(X)$. The goal is to estimate the probability distribution of $X$ by using a minimum number of such sequential samples. This problem has several real-world applications including inference under non-precise information and privacy-preserving statistical estimation. We establish necessary and sufficient conditions on the functions $g_1, \ldots, g_K$ under which asymptotically consistent estimation is possible. We also derive lower bounds on the estimation error as a function of total samples and show that it is order-wise achievable. Leveraging these results, we propose an iterative algorithm that i) chooses the function to observe at each step based on past observations; and ii) combines the obtained samples to estimate $p_X$. The performance of this algorithm is investigated numerically under various scenarios, and shown to outperform baseline approaches.

cs.LG↗

arXiv2018

Slow and Stale Gradients Can Win the Race: Error-Runtime Trade-offs in Distributed SGD

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 and compare distributed SGD algorithms that strike a balance between stragglers and staleness. We also present a new convergence analysis of asynchronous SGD variants without bounded or exponential delay assumptions, and a novel learning rate schedule to compensate for gradient staleness.

stat.ML↗

arXiv2017

On the Service Capacity Region of Accessing Erasure Coded Content

Cloud storage systems generally add redundancy in storing content files such that $K$ files are replicated or erasure coded and stored on $N > K$ nodes. In addition to providing reliability against failures, the redundant copies can be used to serve a larger volume of content access requests. A request for one of the files can be either be sent to a systematic node, or one of the repair groups. In this paper, we seek to maximize the service capacity region, that is, the set of request arrival rates for the $K$ files that can be supported by a coded storage system. We explore two aspects of this problem: 1) for a given erasure code, how to optimally split incoming requests between systematic nodes and repair groups, and 2) choosing an underlying erasure code that maximizes the achievable service capacity region. In particular, we consider MDS and Simplex codes. Our analysis demonstrates that erasure coding makes the system more robust to skews in file popularity than simply replicating a file at multiple servers, and that coding and replication together can make the capacity region larger than either alone.

cs.IT↗

arXiv2017

Efficient Straggler Replication in Large-scale Parallel Computing

In a cloud computing job with many parallel tasks, the tasks on the slowest machines (straggling tasks) become the bottleneck in the job completion. Computing frameworks such as MapReduce and Spark tackle this by replicating the straggling tasks and waiting for any one copy to finish. Despite being adopted in practice, there is little analysis of how replication affects the latency and the cost of additional computing resources. In this paper we provide a framework to analyze this latency-cost trade-off and find the best replication strategy by answering design questions such as: 1) when to replicate straggling tasks, 2) how many replicas to launch, and 3) whether to kill the original copy or not. Our analysis reveals that for certain execution time distributions, a small amount of task replication can drastically reduce both latency as well as the cost of computing resources. We also propose an algorithm to estimate the latency and cost based on the empirical distribution of task execution time. Evaluations using samples in the Google Cluster Trace suggest further latency and cost reduction compared to the existing replication strategy used in MapReduce.

cs.DC↗

arXiv2017

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems

In cloud computing systems, assigning a task to multiple servers and waiting for the earliest copy to finish is an effective method to combat the variability in response time of individual servers, and reduce latency. But adding redundancy may result in higher cost of computing resources, as well as an increase in queueing delay due to higher traffic load. This work helps understand when and how redundancy gives a cost-efficient reduction in latency. For a general task service time distribution, we compare different redundancy strategies in terms of the number of redundant tasks, and time when they are issued and canceled. We get the insight that the log-concavity of the task service time creates a dichotomy of when adding redundancy helps. If the service time distribution is log-convex (i.e. log of the tail probability is convex) then adding maximum redundancy reduces both latency and cost. And if it is log-concave (i.e. log of the tail probability is concave), then less redundancy, and early cancellation of redundant tasks is more effective. Using these insights, we design a general redundancy strategy that achieves a good latency-cost trade-off for an arbitrary service time distribution. This work also generalizes and extends some results in the analysis of fork-join queues.

cs.DC↗

arXiv2015

On Throughput-Smoothness Trade-offs in Streaming Communication

Unlike traditional file transfer where only total delay matters, streaming applications impose delay constraints on each packet and require them to be in order. To achieve fast in-order packet decoding, we have to compromise on the throughput. We study this trade-off between throughput and smoothness in packet decoding. We first consider a point-to-point streaming and analyze how the trade-off is affected by the frequency of block-wise feedback, whereby the source receives full channel state feedback at periodic intervals. We show that frequent feedback can drastically improve the throughput-smoothness trade-off. Then we consider the problem of multicasting a packet stream to two users. For both point-to-point and multicast streaming, we propose a spectrum of coding schemes that span different throughput-smoothness tradeoffs. One can choose an appropriate coding scheme from these, depending upon the delay-sensitivity and bandwidth limitations of the application. This work introduces a novel style of analysis using renewal processes and Markov chains to analyze coding schemes.

cs.IT↗

arXiv2015

Efficient Replication of Queued Tasks for Latency Reduction in Cloud Systems

In cloud computing systems, assigning a job to multiple servers and waiting for the earliest copy to finish is an effective method to combat the variability in response time of individual servers. Although adding redundant replicas always reduces service time, the total computing time spent per job may be higher, thus increasing waiting time in queue. The total time spent per job is also proportional to the cost of computing resources. We analyze how different redundancy strategies, for eg. number of replicas, and the time when they are issued and canceled, affect the latency and computing cost. We get the insight that the log-concavity of the service time distribution is a key factor in determining whether adding redundancy reduces latency and cost. If the service distribution is log-convex, then adding maximum redundancy reduces both latency and cost. And if it is log-concave, then having fewer replicas and canceling the redundant requests early is more effective.

cs.DC↗

arXiv2014

Throughput-Smoothness Trade-offs in Multicasting of an Ordered Packet Stream

An increasing number of streaming applications need packets to be strictly in-order at the receiver. This paper provides a framework for analyzing in-order packet delivery in such applications. We consider the problem of multicasting an ordered stream of packets to two users over independent erasure channels with instantaneous feedback to the source. Depending upon the channel erasures, a packet which is in-order for one user, may be redundant for the other. Thus there is an inter-dependence between throughput and the smoothness of in-order packet delivery to the two users. We use a Markov chain model of packet decoding to analyze these throughput-smoothness trade-offs of the users, and propose coding schemes that can span different points on each trade-off.

cs.IT↗

arXiv2014

Efficient Task Replication for Fast Response Times in Parallel Computation

One typical use case of large-scale distributed computing in data centers is to decompose a computation job into many independent tasks and run them in parallel on different machines, sometimes known as the "embarrassingly parallel" computation. For this type of computation, one challenge is that the time to execute a task for each machine is inherently variable, and the overall response time is constrained by the execution time of the slowest machine. To address this issue, system designers introduce task replication, which sends the same task to multiple machines, and obtains result from the machine that finishes first. While task replication reduces response time, it usually increases resource usage. In this work, we propose a theoretical framework to analyze the trade-off between response time and resource usage. We show that, while in general, there is a tension between response time and resource usage, there exist scenarios where replicating tasks judiciously reduces completion time and resource usage simultaneously. Given the execution time distribution for machines, we investigate the conditions for a scheduling policy to achieve optimal performance trade-off, and propose efficient algorithms to search for optimal or near-optimal scheduling policies. Our analysis gives insights on when and why replication helps, which can be used to guide scheduler design in large-scale distributed computing systems.

cs.DC↗

arXiv2014

The Effect of Block-wise Feedback on the Throughput-Delay Trade-off in Streaming

Unlike traditional file transfer where only total delay matters, streaming applications impose delay constraints on each packet and require them to be in order. To achieve fast in-order packet decoding, we have to compromise on the throughput. We study this trade-off between throughput and in-order decoding delay, and in particular how it is affected by the frequency of block-wise feedback to the source. When there is immediate feedback, we can achieve the optimal throughput and delay simultaneously. But as the feedback delay increases, we have to compromise on at least one of these metrics. We present a spectrum of coding schemes that span different points on the throughput-delay trade-off. Depending upon the delay-sensitivity and bandwidth limitations of the application, one can choose an appropriate operating point on this trade-off.

cs.IT↗

arXiv2013

On the Delay-Storage Trade-off in Content Download from Coded Distributed Storage Systems

In this paper we study how coding in distributed storage reduces expected download time, in addition to providing reliability against disk failures. The expected download time is reduced because when a content file is encoded to add redundancy and distributed across multiple disks, reading only a subset of the disks is sufficient to reconstruct the content. For the same total storage used, coding exploits the diversity in storage better than simple replication, and hence gives faster download. We use a novel fork-join queuing framework to model multiple users requesting the content simultaneously, and derive bounds on the expected download time. Our system model and results are a novel generalization of the fork-join system that is studied in queueing theory literature. Our results demonstrate the fundamental trade-off between the expected download time and the amount of storage space. This trade-off can be used for design of the amount of redundancy required to meet the delay constraints on content delivery.

cs.DC↗

arXiv2012

Coding for Fast Content Download

We study the fundamental trade-off between storage and content download time. We show that the download time can be significantly reduced by dividing the content into chunks, encoding it to add redundancy and then distributing it across multiple disks. We determine the download time for two content access models - the fountain and fork-join models that involve simultaneous content access, and individual access from enqueued user requests respectively. For the fountain model we explicitly characterize the download time, while in the fork-join model we derive the upper and lower bounds. Our results show that coding reduces download time, through the diversity of distributing the data across more disks, even for the total storage used.

cs.IT↗