# On the Global Optimality of Model-Agnostic Meta-Learning

arXiv: https://arxiv.org/abs/2006.13182 · HTML: https://mlsanity.com/paper/2006.13182/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 21 of 21)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining](https://mlsanity.com/paper/2310.08566/) (2023)
- [Simplifying Deep Temporal Difference Learning](https://mlsanity.com/paper/2407.04811/) (2024)
- [Generalization of Model-Agnostic Meta-Learning Algorithms: Recurring and Unseen Tasks](https://mlsanity.com/paper/2102.03832/) (2021)
- [Global Convergence of MAML and Theory-Inspired Neural Architecture Search for Few-Shot Learning](https://mlsanity.com/paper/2203.09137/) (2022)
- [When Is Generalizable Reinforcement Learning Tractable?](https://mlsanity.com/paper/2101.00300/) (2021)
- [Model-Based Offline Meta-Reinforcement Learning with Regularization](https://mlsanity.com/paper/2202.02929/) (2022)
- [Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably?](https://mlsanity.com/paper/2203.03059/) (2022)
- [Robust Fast Adaptation from Adversarially Explicit Task Distribution Generation](https://mlsanity.com/paper/2407.19523/) (2024)
- [Meta-learning with negative learning rates](https://mlsanity.com/paper/2102.00940/) (2021)
- [Learning an Explicit Hyperparameter Prediction Function Conditioned on Tasks](https://mlsanity.com/paper/2107.02378/) (2021)
- [Provable Generalization of Overparameterized Meta-learning Trained with SGD](https://mlsanity.com/paper/2206.09136/) (2022)
- [Neural Collaborative Filtering Bandits via Meta Learning](https://mlsanity.com/paper/2201.13395/) (2022)
- [Memory-Based Optimization Methods for Model-Agnostic Meta-Learning and Personalized Federated Learning](https://mlsanity.com/paper/2106.04911/) (2021)
- [Analytical Survey of Learning with Low-Resource Data: From Analysis to Investigation](https://mlsanity.com/paper/2510.08962/) (2025)
- [Efficient Meta Reinforcement Learning for Preference-based Fast Adaptation](https://mlsanity.com/paper/2211.10861/) (2022)
- [Meta-Reinforcement Learning with Universal Policy Adaptation: Provable Near-Optimality under All-task Optimum Comparator](https://mlsanity.com/paper/2410.09728/) (2024)
- [Exploring the Generalization Capabilities of AID-based Bi-level Optimization](https://mlsanity.com/paper/2411.16081/) (2024)
- [Temporal Variational Implicit Neural Representations](https://mlsanity.com/paper/2506.01544/) (2025)
- [ADDS: Adaptive Differentiable Sampling for Robust Multi-Party Learning](https://mlsanity.com/paper/2110.15522/) (2021)
- [Sharper Analysis of Single-Loop Methods for Bilevel Optimization](https://mlsanity.com/paper/2607.10263/) (2026)

## Abstract (arXiv)

Model-agnostic meta-learning (MAML) formulates meta-learning as a bilevel optimization problem, where the inner level solves each subtask based on a shared prior, while the outer level searches for the optimal shared prior by optimizing its aggregated performance over all the subtasks. Despite its empirical success, MAML remains less understood in theory, especially in terms of its global optimality, due to the nonconvexity of the meta-objective (the outer-level objective). To bridge such a gap between theory and practice, we characterize the optimality gap of the stationary points attained by MAML for both reinforcement learning and supervised learning, where the inner-level and outer-level problems are solved via first-order optimization methods. In particular, our characterization connects the optimality gap of such stationary points with (i) the functional geometry of inner-level objectives and (ii) the representation power of function approximators, including linear models and neural networks. To the best of our knowledge, our analysis establishes the global optimality of MAML with nonconvex meta-objectives for the first time.