# Metalearning Linear Bandits by Prior Update

arXiv: https://arxiv.org/abs/2107.05320 · HTML: https://mlsanity.com/paper/2107.05320/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 19 of 19)

- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Meta-learning of Sequential Strategies](https://mlsanity.com/paper/1905.03030/) (2019)
- [A PAC-Bayesian bound for Lifelong Learning](https://mlsanity.com/paper/1311.2838/) (2013)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [Information-Theoretic Confidence Bounds for Reinforcement Learning](https://mlsanity.com/paper/1911.09724/) (2019)
- [Meta-learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2005.08531/) (2020)
- [Bayesian decision-making under misspecified priors with applications to meta-learning](https://mlsanity.com/paper/2107.01509/) (2021)
- [Meta Dynamic Pricing: Transfer Learning Across Experiments](https://mlsanity.com/paper/1902.10918/) (2019)
- [Accurate Inference for Adaptive Linear Models](https://mlsanity.com/paper/1712.06695/) (2017)
- [An Information-Theoretic Analysis for Thompson Sampling with Many Actions](https://mlsanity.com/paper/1805.11845/) (2018)
- [Prior-free and prior-dependent regret bounds for Thompson Sampling](https://mlsanity.com/paper/1304.5758/) (2013)
- [Are sample means in multi-armed bandits positively or negatively biased?](https://mlsanity.com/paper/1905.11397/) (2019)
- [On the Prior Sensitivity of Thompson Sampling](https://mlsanity.com/paper/1506.03378/) (2015)

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

- [Hierarchical Bayesian Bandits](https://mlsanity.com/paper/2111.06929/) (2021)
- [Mixed-Effect Thompson Sampling](https://mlsanity.com/paper/2205.15124/) (2022)
- [Multi-Task Off-Policy Learning from Bandit Feedback](https://mlsanity.com/paper/2212.04720/) (2022)
- [Thompson Sampling with Diffusion Generative Prior](https://mlsanity.com/paper/2301.05182/) (2023)
- [Offline-to-online hyperparameter transfer for stochastic bandits](https://mlsanity.com/paper/2501.02926/) (2025)
- [reBandit: Random Effects based Online RL algorithm for Reducing Cannabis Use](https://mlsanity.com/paper/2402.17739/) (2024)
- [Diffusion Models Meet Contextual Bandits](https://mlsanity.com/paper/2402.10028/) (2024)
- [Lifelong Bandit Optimization: No Prior and No Regret](https://mlsanity.com/paper/2210.15513/) (2022)
- [Prior-Dependent Allocations for Bayesian Fixed-Budget Best-Arm Identification in Structured Bandits](https://mlsanity.com/paper/2402.05878/) (2024)
- [Meta Learning in Bandits within Shared Affine Subspaces](https://mlsanity.com/paper/2404.00688/) (2024)
- [Thompson Sampling for Robust Transfer in Multi-Task Bandits](https://mlsanity.com/paper/2206.08556/) (2022)
- [Online Meta-Learning in Adversarial Multi-Armed Bandits](https://mlsanity.com/paper/2205.15921/) (2022)
- [Interactive Graph Convolutional Filtering](https://mlsanity.com/paper/2309.01453/) (2023)
- [Co-Exploration and Co-Exploitation via Shared Structure in Multi-Task Bandits](https://mlsanity.com/paper/2512.12693/) (2025)
- [Meta-LinEXP3: Online-within-Online Learning for Adversarial Linear Contextual Bandits](https://mlsanity.com/paper/2609.09907/) (2026)
- [Online LLM Personalization from Pairwise Preferences Across Users](https://mlsanity.com/paper/2610.17203/) (2026)

## Abstract (arXiv)

Fully Bayesian approaches to sequential decision-making assume that problem parameters are generated from a known prior. In practice, such information is often lacking. This problem is exacerbated in setups with partial information, where a misspecified prior may lead to poor exploration and performance. In this work we prove, in the context of stochastic linear bandits and Gaussian priors, that as long as the prior is sufficiently close to the true prior, the performance of the applied algorithm is close to that of the algorithm that uses the true prior. Furthermore, we address the task of learning the prior through metalearning, where a learner updates her estimate of the prior across multiple task instances in order to improve performance on future tasks. We provide an algorithm and regret bounds, demonstrate its effectiveness in comparison to an algorithm that knows the correct prior, and support our theoretical results empirically. Our theoretical results hold for a broad class of algorithms, including Thompson Sampling and Information Directed Sampling.