# More Flexible PAC-Bayesian Meta-Learning by Learning Learning Algorithms

arXiv: https://arxiv.org/abs/2402.04054 · HTML: https://mlsanity.com/paper/2402.04054/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [A PAC-Bayesian bound for Lifelong Learning](https://mlsanity.com/paper/1311.2838/) (2013)
- [Generalization Bounds: Perspectives from Information Theory and PAC-Bayes](https://mlsanity.com/paper/2309.04381/) (2023)
- [Learning-to-Learn Stochastic Gradient Descent with Biased Regularization](https://mlsanity.com/paper/1903.10399/) (2019)
- [Generalization Bounds For Meta-Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2109.14595/) (2021)
- [Generalization Bounds for Meta-Learning via PAC-Bayes and Uniform Stability](https://mlsanity.com/paper/2102.06589/) (2021)
- [Bridging the Gap Between Practice and PAC-Bayes Theory in Few-Shot Meta-Learning](https://mlsanity.com/paper/2105.14099/) (2021)
- [PeFLL: Personalized Federated Learning by Learning to Learn](https://mlsanity.com/paper/2306.05515/) (2023)
- [PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior](https://mlsanity.com/paper/2102.03748/) (2021)
- [Evaluated CMI Bounds for Meta Learning: Tightness and Expressiveness](https://mlsanity.com/paper/2210.06511/) (2022)
- [Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice](https://mlsanity.com/paper/2211.07206/) (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)
- [PAC-Bayes meta-learning with implicit task-specific posteriors](https://mlsanity.com/paper/2003.02455/) (2020)

## Built on by (most cited first, 11 of 11)

- [From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning](https://mlsanity.com/paper/2501.19067/) (2025)
- [Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworks](https://mlsanity.com/paper/2410.13577/) (2024)
- [Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes](https://mlsanity.com/paper/2505.15496/) (2025)
- [Bound to Disagree: Generalization Bounds via Certifiable Surrogates](https://mlsanity.com/paper/2602.23128/) (2026)
- [Learning via Surrogate PAC-Bayes](https://mlsanity.com/paper/2410.10230/) (2024)
- [VERSE: Verified Self-Evolving Optimizer for Agent Harnesses](https://mlsanity.com/paper/2610.02616/) (2026)
- [Model Diffusion for Certifiable Few-shot Transfer Learning](https://mlsanity.com/paper/2502.06970/) (2025)
- [Federated Learning with Unlabeled Clients: Personalization Can Happen in Low Dimensions](https://mlsanity.com/paper/2505.15579/) (2025)
- [An Information-Theoretic Analysis of OOD Generalization in Meta-Reinforcement Learning](https://mlsanity.com/paper/2510.23448/) (2025)
- [Representative Action Selection for Large Action Space: From Bandits to MDPs](https://mlsanity.com/paper/2511.22104/) (2025)
- [A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning](https://mlsanity.com/paper/2605.26341/) (2026)

## Abstract (arXiv)

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous approaches, this could only happen indirectly, by means of learning prior distributions over models. In contrast, the new generalization bounds that we prove express the process of meta-learning much more directly as learning the learning algorithm that should be used for future tasks. The flexibility of our framework makes it suitable to analyze a wide range of meta-learning mechanisms and even design new mechanisms. Other than our theoretical contributions we also show empirically that our framework improves the prediction quality in practical meta-learning mechanisms.