Theoretical Convergence of Multi-Step Model-Agnostic Meta-Learning
This work addresses a theoretical gap for researchers in meta-learning, offering foundational insights but is incremental as it builds on existing MAML methods.
The paper tackles the lack of convergence guarantees for multi-step model-agnostic meta-learning (MAML) by developing a theoretical framework that provides convergence rates and computational complexity for both resampling and finite-sum cases in nonconvex settings, showing that the inner-stage stepsize must scale inversely with the number of inner steps.
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 $ε$-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.