2023/06/06 by Hongchang Gao, Gao, Hongchang
Computer Science · Engineering · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and ELM #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2306.03322
openalex publication_date 2023/06/06 · openalex created_date 2023/06/09 · openalex updated_date 2026/07/28
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.