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

As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algo-rithm has been widely used due to its simplicity and effectiveness. However, the conver-gence 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 algo-rithm 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.

Automated summary

This paper introduces a new theoretical framework to provide convergence guarantees for two types of objective functions for the MAML algorithm, for both resampling and finite-sum cases. The results suggest that for N-step MAML, the inner-stage stepsize needs to be inversely proportional to the number of inner-stage steps chosen.