skip to main content

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Friday, December 13 until 2:00 AM ET on Saturday, December 14 due to maintenance. We apologize for the inconvenience.


Title: On the worst-case communication overhead for distributed data shuffling
Distributed learning platforms for processing large scale data-sets are becoming increasingly prevalent. In typical distributed implementations, a centralized master node breaks the data-set into smaller batches for parallel processing across distributed workers to achieve speed-up and efficiency. Several computational tasks are of sequential nature, and involve multiple passes over the data. At each iteration over the data, it is common practice to randomly re-shuffle the data at the master node, assigning different batches for each worker to process. This random re-shuffling operation comes at the cost of extra communication overhead, since at each shuffle, new data points need to be delivered to the distributed workers. In this paper, we focus on characterizing the information theoretically optimal communication overhead for the distributed data shuffling problem. We propose a novel coded data delivery scheme for the case of no excess storage, where every worker can only store the assigned data batches under processing. Our scheme exploits a new type of coding opportunity and is applicable to any arbitrary shuffle, and for any number of workers. We also present information theoretic lower bounds on the minimum communication overhead for data shuffling, and show that the proposed scheme matches this lower bound for the worst-case communication overhead.  more » « less
Award ID(s):
1651492
PAR ID:
10048925
Author(s) / Creator(s):
;
Date Published:
Journal Name:
54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Page Range / eLocation ID:
961 to 968
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Data shuffling is one of the fundamental building blocks for distributed learning algorithms, that increases the statistical gain for each step of the learning process. In each iteration, different shuffled data points are assigned by a central node to a distributed set of workers to perform local computations, which leads to communication bottlenecks. The focus of this paper is on formalizing and understanding the fundamental information-theoretic tradeoff between storage (per worker) and the worst-case communication overhead for the data shuffling problem. We completely characterize the information theoretic tradeoff for K = 2, and K = 3 workers, for any value of storage capacity, and show that increasing the storage across workers can reduce the communication overhead by leveraging coding. We propose a novel and systematic data delivery and storage update strategy for each data shuffle iteration, which preserves the structural properties of the storage across the workers, and aids in minimizing the communication overhead in subsequent data shuffling iterations. 
    more » « less
  2. Data shuffling between distributed workers is one of the critical steps in implementing large-scale learning algorithms. The focus of this work is to understand the fundamental trade-off between the amount of storage and the communication overhead for distributed data shuffling. We first present an information theoretic formulation for the data shuffling problem, accounting for the underlying problem parameters (i.e., number of workers, K, number of data points, N, and the available storage, S per node). Then, we derive an information theoretic lower bound on the communication overhead for data shuffling as a function of these parameters. Next, we present a novel coded communication scheme and show that the resulting communication overhead of the proposed scheme is within a multiplicative factor of at most 2 from the lower bound. Furthermore, we introduce an improved aligned coded shuffling scheme, which achieves the optimal storage vs communication trade-off for K <; 5, and further reduces the maximum multiplicative gap down to 7/6, for K ≥ 5. 
    more » « less
  3. null (Ed.)
    This paper studies the distributed linearly separable computation problem, which is a generalization of many existing distributed computing problems such as distributed gradient coding and distributed linear transform. A master asks N distributed workers to compute a linearly separable function of K datasets, which is a set of Kc linear combinations of K equal-length messages (each message is a function of one dataset). We assign some datasets to each worker in an uncoded manner, who then computes the corresponding messages and returns some function of these messages, such that from the answers of any Nr out of N workers the master can recover the task function with high probability. In the literature, the specific case where Kc = 1 or where the computation cost is minimum has been considered. In this paper, we focus on the general case (i.e., general Kc and general computation cost) and aim to find the minimum communication cost. We first propose a novel converse bound on the communication cost under the constraint of the popular cyclic assignment (widely considered in the literature), which assigns the datasets to the workers in a cyclic way. Motivated by the observation that existing strategies for distributed computing fall short of achieving the converse bound, we propose a novel distributed computing scheme for some system parameters. The proposed computing scheme is optimal for any assignment when Kc is large and is optimal under the cyclic assignment when the numbers of workers and datasets are equal or Kc is small. In addition, it is order optimal within a factor of 2 under the cyclic assignment for the remaining cases. 
    more » « less
  4. We consider distributed gradient computation, where both data and computation are distributed among m worker machines, t of which can be Byzantine adversaries, and a designated (master) node computes the model/parameter vector for generalized linear models, iteratively, using proximal gradient descent (PGD), of which gradient descent (GD) is a special case. The Byzantine adversaries can (collaboratively) deviate arbitrarily from their gradient computation. To solve this, we propose a method based on data encoding and (real) error correction to combat the adversarial behavior. We can tolerate up to t <= (m−1)/2 corrupt worker nodes, which is 2 information-theoretically optimal. Our method does not assume any probability distribution on the data. We develop a sparse encoding scheme which enables computationally efficient data encoding. We demonstrate a trade-off between the number of adversaries tolerated and the resource requirement (storage and computational complexity). As an example, our scheme incurs a constant overhead (storage and computational complexity) over that required by the distributed PGD algorithm, without adversaries, for t <= m . Our encoding works as efficiently in the streaming data setting as it does in the offline setting, in which all the data is available beforehand. 
    more » « less
  5. null (Ed.)
    In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear convergence. To our knowledge, this is the first distributed asynchronous algorithm with superlinear convergence guarantees. Our algorithm is communication-efficient in the sense that at every iteration the master node and workers communicate vectors of size 𝑂(𝑝), where 𝑝 is the dimension of the decision variable. The proposed method is based on a distributed asynchronous averaging scheme of decision vectors and gradients in a way to effectively capture the local Hessian information of the objective function. Our convergence theory supports asynchronous computations subject to both bounded delays and unbounded delays with a bounded time-average. Unlike in the majority of asynchronous optimization literature, we do not require choosing smaller stepsize when delays are huge. We provide numerical experiments that match our theoretical results and showcase significant improvement comparing to state-of-the-art distributed algorithms. 
    more » « less