Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms

  • Tao Sun National University of Defense Technology
  • Penghang Yin National University of Defense Technology
  • Dongsheng Li National University of Defense Technology
  • Chun Huang National University of Defense Technology
  • Lei Guan National University of Defense Technology
  • Hao Jiang National University of Defense Technology

Abstract

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable.

Published
2019-07-17
Section
AAAI Technical Track: Machine Learning