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

2020/02/18 by Kaiyi Ji, Junjie Yang, Ji, Kaiyi +3 · 1 citation
Computer Science · #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning and Data Classification #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2002.07836

openalex publication_date 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Adam: A Method for Stochastic Optimization
• Trust Region Policy Optimization
• Prototypical Networks for Few-shot Learning
• Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks
• Meta-SGD: Learning to Learn Quickly for Few-Shot Learning
• Incremental Learning-to-Learn with Statistical Guarantees
• On First-Order Meta-Learning Algorithms
• Federated Meta-Learning with Fast Convergence and Efficient Communication
• Provable Meta-Learning of Linear Representations
• Few-Shot Learning via Learning the Representation, Provably
• Multi-step Estimation for Gradient-based Meta-learning
• On the Global Optimality of Model-Agnostic Meta-Learning
• Convergence of Meta-Learning with Task-Specific Adaptation over Partial Parameters

Cited by

• UFO-BLO: Unbiased First-Order Bilevel Optimization

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