On the fine-grained complexity of empirical risk minimization: Kernel methods and neural networks
Name
7018-on-the-fine-grained-complexity-of-empirical-risk-minimization-kernel-methods-and-neural-networks.pdf
Description
Published version
Size
323.64 KB
Format
Unknown
Checksum (MD5)
ed8543d0f3c2140d0afa488fcfdde102
Author(s)
Indyk, Piotr
Schmidt, Ludwig
Backurs, Arturs
Date Issued
December 2017
Journal
NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems
Publisher
Curran Associates Inc.
Citation
Indyk, Piotr, Schmidt, Ludwig and Backurs, Arturs. 2017. "On the fine-grained complexity of empirical risk minimization: Kernel methods and neural networks."
Version
Final published version
Abstract
© 2017 Neural information processing systems foundation. All rights reserved. Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there is a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM is still not understood. We address this issue for multiple popular ERM problems including kernel SVMs, kernel ridge regression, and training the final layer of a neural network. In particular, we give conditional hardness results for these problems based on complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis. Under these assumptions, we show that there are no algorithms that solve the aforementioned ERM problems to high accuracy in sub-quadratic time. We also give similar hardness results for computing the gradient of the empirical loss, which is the main computational burden in many non-convex learning tasks.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/7018-on-the-fine-grained-complexity-of-empirical-risk-minimization-kernel-methods-and-neural-networks
