# Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably?

arXiv: https://arxiv.org/abs/2203.03059 · HTML: https://mlsanity.com/paper/2203.03059/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 61 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 30 of 41)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Task2Vec: Task Embedding for Meta-Learning](https://mlsanity.com/paper/1902.03545/) (2019)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Meta-Learning Probabilistic Inference For Prediction](https://mlsanity.com/paper/1805.09921/) (2018)
- [Provably Faster Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2106.04692/) (2021)
- [Multimodal Model-Agnostic Meta-Learning via Task-Aware Modulation](https://mlsanity.com/paper/1910.13616/) (2019)
- [Meta-Learning without Memorization](https://mlsanity.com/paper/1912.03820/) (2019)
- [ProMP: Proximal Meta-Policy Search](https://mlsanity.com/paper/1810.06784/) (2018)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [Personalizing Dialogue Agents via Meta-Learning](https://mlsanity.com/paper/1905.10033/) (2019)
- [Unsupervised Learning via Meta-Learning](https://mlsanity.com/paper/1810.02334/) (2018)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [Provable Guarantees for Gradient-Based Meta-Learning](https://mlsanity.com/paper/1902.10644/) (2019)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [Solving Stochastic Compositional Optimization is Nearly as Easy as Solving Stochastic Optimization](https://mlsanity.com/paper/2008.10847/) (2020)
- [Continuous Meta-Learning without Tasks](https://mlsanity.com/paper/1912.08866/) (2019)
- [Generalization Bounds For Meta-Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2109.14595/) (2021)

## Built on by (most cited first, 13 of 13)

- [Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning](https://mlsanity.com/paper/2206.03996/) (2022)
- [Predicting Configuration Performance in Multiple Environments with Sequential Meta-learning](https://mlsanity.com/paper/2402.03183/) (2024)
- [Understanding Benign Overfitting in Gradient-Based Meta Learning](https://mlsanity.com/paper/2206.13482/) (2022)
- [Provable Generalization of Overparameterized Meta-learning Trained with SGD](https://mlsanity.com/paper/2206.09136/) (2022)
- [Bayes meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes](https://mlsanity.com/paper/2302.11709/) (2023)
- [Meta-Learning with Generalized Ridge Regression: High-dimensional Asymptotics, Optimality and Hyper-covariance Estimation](https://mlsanity.com/paper/2403.19720/) (2024)
- [Scalable Bayesian Meta-Learning through Generalized Implicit Gradients](https://mlsanity.com/paper/2303.17768/) (2023)
- [Theoretical Characterization of the Generalization Performance of Overfitted Meta-Learning](https://mlsanity.com/paper/2304.04312/) (2023)
- [Personalized Federated Learning via Amortized Bayesian Meta-Learning](https://mlsanity.com/paper/2307.02222/) (2023)
- [Hypernetwork approach to Bayesian MAML](https://mlsanity.com/paper/2210.02796/) (2022)
- [A Hierarchical Bayesian Model for Deep Few-Shot Meta Learning](https://mlsanity.com/paper/2306.09702/) (2023)
- [Reducing Variance in Meta-Learning via Laplace Approximation for Regression Tasks](https://mlsanity.com/paper/2410.01476/) (2024)
- [Domain-Generalization to Improve Learning in Meta-Learning Algorithms](https://mlsanity.com/paper/2508.09418/) (2025)

## Abstract (arXiv)

Meta learning aims at learning a model that can quickly adapt to unseen tasks. Widely used meta learning methods include model agnostic meta learning (MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling uncertainty, Bayesian MAML often has advantageous empirical performance. However, the theoretical understanding of Bayesian MAML is still limited, especially on questions such as if and when Bayesian MAML has provably better performance than MAML. In this paper, we aim to provide theoretical justifications for Bayesian MAML's advantageous performance by comparing the meta test risks of MAML and Bayesian MAML. In the meta linear regression, under both the distribution agnostic and linear centroid cases, we have established that Bayesian MAML indeed has provably lower meta test risks than MAML. We verify our theoretical results through experiments.