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worker (i.e., increasing N by 1) LCC can increase the resiliency to stragglers by 1 or increase the
robustness to malicious servers by 1/2, while maintaining the privacy constraint. Hence, this result
essentially extends the well-known optimal scaling of error-correcting codes (i.e., adding one parity
can provide robustness against one erasure or 1/2 error in optimal maximum distance separable
codes) to the distributed secure computing paradigm.
We prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency,
security, and privacy. In other words, any computing scheme (under certain complexity constrains on
the encoding and decoding designs) can achieve (S, A, T) if and only if (K+T−1) deg f+S+2A+1
N.1 This result further extends the scaling law in coding theory to private computing, showing that
any additional worker enables data privacy against 1/degf additional colluding workers.
Our general theoretical guarantees for LCC is specialized in [20] in the context of least-squares
linear regression, which is one of the elemental learning tasks. It is shown 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.
Related works. There has recently been a surge of interest on using coding theoretic approaches
to alleviate key bottlenecks (e.g., stragglers, bandwidth, and security) in distributed machine learning
applications (e.g., [1,3,14,22,23,96–102]). As we discuss in more detail in Section 6.2.1, the proposed
LCC scheme significantly advances prior works in this area by 1) generalizing coded computing to
arbitrary multivariate polynomial computations, which are of particular importance in learning
applications; 2) extending the application of coded computing to secure and private computing; 3)
reducing the computation/communication load in distributed computing (and distributed learning)
by factors that scale with the problem size, without compromising security and privacy guarantees;
and 4) enabling 2.36×-12.65× speedup over the state-of-the-art in distributed least-squares linear
regression in cloud networks.
Secure multiparty computing (MPC) and secure/private Machine Learning (e.g., [103, 104]) are
also extensively studied topics that address a problem setting similar to LCC. As we elaborate in
Section 6.2.1, compared with conventional methods in this area (e.g., the celebrated BGW scheme
for secure and private MPC [103]), LCC achieves substantial reduction in the amount of randomness,
storage overhead, and computation complexity.
1More accurately, when N < Kdegf −1, we prove that the optimal tradeoff is instead given by K(S +2A+deg f ·
T + 1) N, which can be achieved by a variation of the LCC scheme, as described in Appendix C.3.
69
Object Description
| Title | Coded computing: a transformative framework for resilient, secure, private, and communication efficient large scale distributed computing |
| Author | Yu, Qian |
| Author email | qyu880@usc.edu;qianyu0929@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2020-03-24 |
| Date submitted | 2020-08-04 |
| Date approved | 2020-08-05 |
| Restricted until | 2020-08-05 |
| Date published | 2020-08-05 |
| Advisor (committee chair) | Avestimehr, Salman |
| Advisor (committee member) |
Luo, HaiPeng Ortega, Antonio Soltanolkotabi, Mahdi |
| Abstract | Modern computing applications often require handling massive amounts of data in a distributed setting, where significant issues on resiliency, security, or privacy could arise. This dissertation presents new computing designs and optimality proofs, that address these issues through coding and information-theoretic approaches. ❧ The first part of this thesis focuses on a standard setup, where the computation is carried out using a set of worker nodes, each can store and process a fraction of the input dataset. The goal is to find computation schemes for providing the optimal resiliency against stragglers given the computation task, the number of workers, and the functions computed by the workers. The resiliency is measured in terms of the recovery threshold, defined as the minimum number of workers to wait for in order to compute the final result. We propose optimal solutions for broad classes of computation tasks, from basic building blocks such as matrix multiplication (entangled polynomial codes), Fourier transform (coded FFT), and convolution (polynomial code), to general functions such as multivariate polynomial evaluation (Lagrange coded computing). We develop optimal computing strategies by introducing a general coding framework called “polynomial coded computing”, to exploit the algebraic structure of the computation task and create computation redundancy in a novel coded form across workers. Polynomial coded computing allows for order-wise improvements over the state of the arts and significantly generalizes classical coding-theoretic results to go beyond linear computations. The encoding and decoding process of polynomial coded computing designs can be mapped to polynomial evaluation and interpolation, which can be computed efficiently. ❧ Then we show that polynomial coded computing can be extended to provide unified frameworks that also enable security and privacy in the computation. We present the optimal designs for three important problems: distributed matrix multiplication, multivariate polynomial evaluation, and gradient-type computation. We prove their optimality by developing information-theoretic and linear-algebraic converse bounding techniques. ❧ Finally, we consider the problem of coding for communication reduction. In the context of distributed computation, we focus on a MapReduce-type framework, where the workers need to shuffle their intermediate results to finish the computation. We aim to understand how to optimally exploit extra computing power to reduce communication, i.e., to establish a fundamental tradeoff between computation and communication. We prove a lower bound on the needed communication load for general allocation of the task assignments, by introducing a novel information-theoretic converse bounding approach. The presented lower bound exactly matches the inverse-proportional coding gain achieved by coded distributed computing schemes, completely characterizing the optimal computation-communication tradeoff. The proposed converse bounding approach strictly improves conventional cut-set bounds and can be widely applied to prove exact optimally results for more general settings, as well as more classical communication problems. We also investigate a problem called coded caching, where a single server is connected to multiple users in a cache network through a shared bottleneck link. Each user has an isolated memory that can be used to prefetch content. Then the server needs to deliver users’ demands efficiently in a following delivery phase. We propose caching and delivery designs that improve the state-of-the-art schemes under both centralized and decentralized settings, for both peak and average communication rates. Moreover, by developing information-theoretic bounds, we prove the proposed designs are exactly optimal among all schemes that use uncoded prefetching, and optimal within a factor of 2.00884 among schemes with coded prefetching. |
| Keyword | coding theory; information theory; distributed computing; security; privacy; matrix multiplication; caching |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Yu, Qian |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-YuQian-8883.pdf |
| Archival file | Volume13/etd-YuQian-8883.pdf |
Description
| Title | Page 84 |
| Full text | worker (i.e., increasing N by 1) LCC can increase the resiliency to stragglers by 1 or increase the robustness to malicious servers by 1/2, while maintaining the privacy constraint. Hence, this result essentially extends the well-known optimal scaling of error-correcting codes (i.e., adding one parity can provide robustness against one erasure or 1/2 error in optimal maximum distance separable codes) to the distributed secure computing paradigm. We prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy. In other words, any computing scheme (under certain complexity constrains on the encoding and decoding designs) can achieve (S, A, T) if and only if (K+T−1) deg f+S+2A+1 N.1 This result further extends the scaling law in coding theory to private computing, showing that any additional worker enables data privacy against 1/degf additional colluding workers. Our general theoretical guarantees for LCC is specialized in [20] in the context of least-squares linear regression, which is one of the elemental learning tasks. It is shown 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. Related works. There has recently been a surge of interest on using coding theoretic approaches to alleviate key bottlenecks (e.g., stragglers, bandwidth, and security) in distributed machine learning applications (e.g., [1,3,14,22,23,96–102]). As we discuss in more detail in Section 6.2.1, the proposed LCC scheme significantly advances prior works in this area by 1) generalizing coded computing to arbitrary multivariate polynomial computations, which are of particular importance in learning applications; 2) extending the application of coded computing to secure and private computing; 3) reducing the computation/communication load in distributed computing (and distributed learning) by factors that scale with the problem size, without compromising security and privacy guarantees; and 4) enabling 2.36×-12.65× speedup over the state-of-the-art in distributed least-squares linear regression in cloud networks. Secure multiparty computing (MPC) and secure/private Machine Learning (e.g., [103, 104]) are also extensively studied topics that address a problem setting similar to LCC. As we elaborate in Section 6.2.1, compared with conventional methods in this area (e.g., the celebrated BGW scheme for secure and private MPC [103]), LCC achieves substantial reduction in the amount of randomness, storage overhead, and computation complexity. 1More accurately, when N < Kdegf −1, we prove that the optimal tradeoff is instead given by K(S +2A+deg f · T + 1) N, which can be achieved by a variation of the LCC scheme, as described in Appendix C.3. 69 |
