skip to main content

Title: Lagrange Coded Computing: Optimal Design for Resiliency, Security, and Privacy
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 computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to 13.43×, and also achieves a 2.36×-12.65× speedup over the state-of-the-art straggler mitigation strategies.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
International Conference on Artificial Intelligence and Statistics (AISTATS 2019)
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Stragglers, Byzantine workers, and data privacy are the main bottlenecks in distributed cloud computing. Some prior works proposed coded computing strategies to jointly address all three challenges. They require either a large number of workers, a significant communication cost or a significant computational complexity to tolerate Byzantine workers. Much of the overhead in prior schemes comes from the fact that they tightly couple coding for all three problems into a single framework. In this paper, we propose Adaptive Verifiable Coded Computing (AVCC) framework that decouples the Byzantine node detection challenge from the straggler tolerance. AVCC leverages coded computing just for handling stragglers and privacy, and then uses an orthogonal approach that leverages verifiable computing to mitigate Byzantine workers. Furthermore, AVCC dynamically adapts its coding scheme to trade-off straggler tolerance with Byzantine protection. We evaluate AVCC on a compute-intensive distributed logistic regression application. Our experiments show that AVCC achieves up to 4.2× speedup and up to 5.1% accuracy improvement over the state-of-the-art Lagrange coded computing approach (LCC). AVCC also speeds up the conventional uncoded implementation of distributed logistic regression by up to 7.6×, and improves the test accuracy by up to 12.1%. 
    more » « less
  2. Machine learning today involves massive distributed computations running on cloud servers, which are highly susceptible to slowdown or straggling. Recent work has demonstrated the effectiveness of erasure codes in mitigating such slowdown for linear computations, by adding redundant computations such that the entire computation can be recovered as long as a subset of nodes finish their assigned tasks. However, most machine learning algorithms typically involve non-linear computations that cannot be directly handled by these coded computing approaches. In this work, we propose a coded computing strategy for mitigating the effect of stragglers on non-linear distributed computations. Our strategy relies on the observation that many expensive non-linear functions can be decomposed into sums of cheap non-linear functions. We show that erasure codes, specifically rateless codes can be used to generate and compute random linear combinations of these functions at the nodes such that the original function can be computed as long as a subset of nodes return their computations. Simulations and experiments on AWS Lambda demonstrate the superiority of our approach over various uncoded baselines. 
    more » « less
  3. null (Ed.)
    Abstract Edge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive tasks by employing erasure codes and offloading these tasks to other devices for computation. Coded computation is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account (1) the privacy requirements of IoT applications and devices, and (2) the heterogeneous and time-varying resources of edge devices. We show that PRAC outperforms known secure coded computing methods when resources are heterogeneous. We provide theoretical guarantees on the performance of PRAC and its comparison to baselines. Moreover, we confirm our theoretical results through simulations and implementations on Android-based smartphones. 
    more » « less
  4. 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 re-defined with each elastic event. Computation assignment algorithms are used to minimize the computation time given computation speeds of different machines. While previous studies of heterogeneous CSEC do not include stragglers - the slow machines during the computation, we develop a new framework in heterogeneous CSEC that introduces straggler tolerance. Based on this framework, we design a novel algorithm using our previously proposed approach for heterogeneous CSEC such that the system can handle any subset of stragglers of a specified size while minimizing the computation time. Furthermore, we establish a trade-off in computation time and straggler tolerance. Another major limitation of existing CSEC designs is the lack of practical evaluations using real applications. In this paper, we evaluate the performance of our designs on Amazon EC2 for applications of the power iteration and linear regression. Evaluation results show that the proposed heterogeneous CSEC algorithms outperform the state-of-the-art designs by more than 30%. 
    more » « less
  5. Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower computations). In many scenarios, instead of exact computation, approximate matrix multiplication, i.e., allowing for a tolerable error is also sufficient. Such approximate schemes make use of randomization techniques to speed up the computation process. In this paper, we initiate the study of approximate coded matrix multiplication, and investigate the joint synergies offered by randomization and coding. Specifically, we propose two coded randomized sampling schemes that use (a) codes to achieve a desired recovery threshold and (b) random sampling to obtain approximation of the matrix multiplication. Tradeoffs between the recovery threshold and approximation error obtained through random sampling are investigated for a class of coded matrix multiplication schemes. 
    more » « less