TY - JOUR AU - Sun, Tao AU - Yin, Penghang AU - Li, Dongsheng AU - Huang, Chun AU - Guan, Lei AU - Jiang, Hao PY - 2019/07/17 Y2 - 2024/03/29 TI - Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms JF - Proceedings of the AAAI Conference on Artificial Intelligence JA - AAAI VL - 33 IS - 01 SE - AAAI Technical Track: Machine Learning DO - 10.1609/aaai.v33i01.33015033 UR - https://ojs.aaai.org/index.php/AAAI/article/view/4435 SP - 5033-5040 AB - <p>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 <em>O</em>(1/<em>k</em>) 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.</p> ER -