Decentralized Multi-Level Compositional Optimization Algorithms with Level-Independent Convergence Rate

Hongchang Gao
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4402-4410, 2024.

Abstract

Stochastic multi-level compositional optimization problems cover many new machine learning paradigms, e.g., multi-step model-agnostic meta-learning, which require efficient optimization algorithms for large-scale data. This paper studies the decentralized stochastic multi-level optimization algorithm, which is challenging because the multi-level structure and decentralized communication scheme may make the number of levels significantly affect the order of the convergence rate. To this end, we develop two novel decentralized optimization algorithms to optimize the multi-level compositional optimization problem. Our theoretical results show that both algorithms can achieve the level-independent convergence rate for nonconvex problems under much milder conditions compared with existing single-machine algorithms. To the best of our knowledge, this is the first work that achieves the level-independent convergence rate under the decentralized setting. Moreover, extensive experiments confirm the efficacy of our proposed algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-gao24b, title = { Decentralized Multi-Level Compositional Optimization Algorithms with Level-Independent Convergence Rate }, author = {Gao, Hongchang}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {4402--4410}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/gao24b/gao24b.pdf}, url = {https://proceedings.mlr.press/v238/gao24b.html}, abstract = { Stochastic multi-level compositional optimization problems cover many new machine learning paradigms, e.g., multi-step model-agnostic meta-learning, which require efficient optimization algorithms for large-scale data. This paper studies the decentralized stochastic multi-level optimization algorithm, which is challenging because the multi-level structure and decentralized communication scheme may make the number of levels significantly affect the order of the convergence rate. To this end, we develop two novel decentralized optimization algorithms to optimize the multi-level compositional optimization problem. Our theoretical results show that both algorithms can achieve the level-independent convergence rate for nonconvex problems under much milder conditions compared with existing single-machine algorithms. To the best of our knowledge, this is the first work that achieves the level-independent convergence rate under the decentralized setting. Moreover, extensive experiments confirm the efficacy of our proposed algorithms. } }
Endnote
%0 Conference Paper %T Decentralized Multi-Level Compositional Optimization Algorithms with Level-Independent Convergence Rate %A Hongchang Gao %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-gao24b %I PMLR %P 4402--4410 %U https://proceedings.mlr.press/v238/gao24b.html %V 238 %X Stochastic multi-level compositional optimization problems cover many new machine learning paradigms, e.g., multi-step model-agnostic meta-learning, which require efficient optimization algorithms for large-scale data. This paper studies the decentralized stochastic multi-level optimization algorithm, which is challenging because the multi-level structure and decentralized communication scheme may make the number of levels significantly affect the order of the convergence rate. To this end, we develop two novel decentralized optimization algorithms to optimize the multi-level compositional optimization problem. Our theoretical results show that both algorithms can achieve the level-independent convergence rate for nonconvex problems under much milder conditions compared with existing single-machine algorithms. To the best of our knowledge, this is the first work that achieves the level-independent convergence rate under the decentralized setting. Moreover, extensive experiments confirm the efficacy of our proposed algorithms.
APA
Gao, H.. (2024). Decentralized Multi-Level Compositional Optimization Algorithms with Level-Independent Convergence Rate . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:4402-4410 Available from https://proceedings.mlr.press/v238/gao24b.html.

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