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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 33 / No. 1: AAAI-19, IAAI-19, EAAI-20

Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms

February 1, 2023

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Authors

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


DOI:

10.1609/aaai.v33i01.33015033


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.

Topics: AAAI

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HOW TO CITE:

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms Proceedings of the AAAI Conference on Artificial Intelligence (2019) 5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms AAAI 2019, 5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang (2019). Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms. Proceedings of the AAAI Conference on Artificial Intelligence, 5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. 2019. Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms. "Proceedings of the AAAI Conference on Artificial Intelligence". 5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. (2019) "Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms", Proceedings of the AAAI Conference on Artificial Intelligence, p.5033-5040

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang, "Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms", AAAI, p.5033-5040, 2019.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. "Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. "Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 5033-5040.

Tao Sun||Penghang Yin||Dongsheng Li||Chun Huang||Lei Guan||Hao Jiang. Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms. AAAI[Internet]. 2019[cited 2023]; 5033-5040.


ISSN: 2374-3468


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