Theoretical Convergence of Multi-Step Model-Agnostic Meta-Learning

• URL: http://arxiv.org/abs/2002.07836v3
• Date: Mon, 13 Jul 2020 04:03:09 GMT
• Title: Theoretical Convergence of Multi-Step Model-Agnostic Meta-Learning
• Authors: Kaiyi Ji, Junjie Yang, Yingbin Liang
• Abstract summary: We develop a new theoretical framework to provide convergence guarantee for the general multi-step MAML algorithm. In particular, our results suggest that an inner-stage step needs to be chosen inversely proportional to $N$ of inner-stage steps in order for $N$ MAML to have guaranteed convergence.
• Score: 63.64636047748605
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this paper, we develop a new theoretical framework to provide such convergence guarantee for two types of objective functions that are of interest in practice: (a) resampling case (e.g., reinforcement learning), where loss functions take the form in expectation and new data are sampled as the algorithm runs; and (b) finite-sum case (e.g., supervised learning), where loss functions take the finite-sum form with given samples. For both cases, we characterize the convergence rate and the computational complexity to attain an $\epsilon$-accurate solution for multi-step MAML in the general nonconvex setting. In particular, our results suggest that an inner-stage stepsize needs to be chosen inversely proportional to the number $N$ of inner-stage steps in order for $N$-step MAML to have guaranteed convergence. From the technical perspective, we develop novel techniques to deal with the nested structure of the meta gradient for multi-step MAML, which can be of independent interest.

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