Stochastic Multi-Level Compositional Optimization Algorithms over Networks with Level-Independent Convergence Rate

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 applications. 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 affect the order of the convergence rate. To this end, we develop two novel decentralized optimization algorithms to deal with the multi-level function and its gradient. 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.