# Incremental Learning-to-Learn with Statistical Guarantees

arXiv: https://arxiv.org/abs/1803.08089 · HTML: https://mlsanity.com/paper/1803.08089/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 16 of 16)

- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Provable Representation Learning for Imitation Learning via Bi-level Optimization](https://mlsanity.com/paper/2002.10544/) (2020)
- [How Fine-Tuning Allows for Effective Meta-Learning](https://mlsanity.com/paper/2105.02221/) (2021)
- [An Information-Theoretic Analysis of In-Context Learning](https://mlsanity.com/paper/2401.15530/) (2024)
- [On the Power of Multitask Representation Learning in Linear MDP](https://mlsanity.com/paper/2106.08053/) (2021)
- [Multi-task Representation Learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2202.10066/) (2022)
- [Nearly Minimax Algorithms for Linear Bandits with Shared Representation](https://mlsanity.com/paper/2203.15664/) (2022)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [Conditional Meta-Learning of Linear Representations](https://mlsanity.com/paper/2103.16277/) (2021)
- [A Representation Learning Perspective on the Importance of Train-Validation Splitting in Meta-Learning](https://mlsanity.com/paper/2106.15615/) (2021)
- [An Information-Theoretic Analysis of the Impact of Task Similarity on Meta-Learning](https://mlsanity.com/paper/2101.08390/) (2021)
- [Non-stationary Bandits and Meta-Learning with a Small Set of Optimal Arms](https://mlsanity.com/paper/2202.13001/) (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 Representation Learning with Contextual Linear Bandits](https://mlsanity.com/paper/2205.15100/) (2022)
- [Towards Auto-Regressive Next-Token Prediction: In-Context Learning Emerges from Generalization](https://mlsanity.com/paper/2502.17024/) (2025)
- [On regret bounds for continual single-index learning](https://mlsanity.com/paper/2102.12961/) (2021)

## Abstract (arXiv)

In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are presented sequentially and the algorithm needs to adapt incrementally to improve its performance on future tasks. Key to this setting is for the algorithm to rapidly incorporate new observations into the model as they arrive, without keeping them in memory. We focus on the case where the underlying algorithm is ridge regression parameterized by a positive semidefinite matrix. We propose to learn this matrix by applying a stochastic strategy to minimize the empirical error incurred by ridge regression on future tasks sampled from the meta distribution. We study the statistical properties of the proposed algorithm and prove non-asymptotic bounds on its excess transfer risk, that is, the generalization performance on new tasks from the same meta distribution. We compare our online learning-to-learn approach with a state of the art batch method, both theoretically and empirically.