# Anytime Model Selection in Linear Bandits

arXiv: https://arxiv.org/abs/2307.12897 · HTML: https://mlsanity.com/paper/2307.12897/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 27 of 27)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Explore no more: Improved high-probability regret bounds for non-stochastic bandits](https://mlsanity.com/paper/1506.03271/) (2015)
- [Corralling a Band of Bandit Algorithms](https://mlsanity.com/paper/1612.06246/) (2016)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Model Selection in Contextual Stochastic Bandit Problems](https://mlsanity.com/paper/2003.01704/) (2020)
- [Kernel-based methods for bandit convex optimization](https://mlsanity.com/paper/1607.03084/) (2016)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Model selection for contextual bandits](https://mlsanity.com/paper/1906.00531/) (2019)
- [Bias no more: high-probability data-dependent regret bounds for adversarial bandits and MDPs](https://mlsanity.com/paper/2006.08040/) (2020)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Parameter-free online learning via model selection](https://mlsanity.com/paper/1801.00101/) (2017)
- [Celer: a Fast Solver for the Lasso with Dual Extrapolation](https://mlsanity.com/paper/1802.07481/) (2018)
- [Corralling a Larger Band of Bandits: A Case Study on Switching Regret for Linear Bandits](https://mlsanity.com/paper/2202.06151/) (2022)
- [Bayesian Optimization for Synthetic Gene Design](https://mlsanity.com/paper/1505.01627/) (2015)
- [A Simple Unified Framework for High Dimensional Bandit Problems](https://mlsanity.com/paper/2102.09626/) (2021)
- [Online Active Model Selection for Pre-trained Classifiers](https://mlsanity.com/paper/2010.09818/) (2020)
- [PopArt: Efficient Sparse Regression and Experimental Design for Optimal Sparse Linear Bandits](https://mlsanity.com/paper/2210.15345/) (2022)
- [Bayesian Optimization with Dimension Scheduling: Application to Biological Systems](https://mlsanity.com/paper/1511.05385/) (2015)
- [Exploration in Linear Bandits with Rich Action Sets and its Implications for Inference](https://mlsanity.com/paper/2207.11597/) (2022)
- [Neural Design for Genetic Perturbation Experiments](https://mlsanity.com/paper/2207.12805/) (2022)
- [Best of many worlds: Robust model selection for online supervised learning](https://mlsanity.com/paper/1805.08562/) (2018)
- [Feature and Parameter Selection in Stochastic Linear Bandits](https://mlsanity.com/paper/2106.05378/) (2021)
- [Meta-Learning Hypothesis Spaces for Sequential Decision-making](https://mlsanity.com/paper/2202.00602/) (2022)
- [Lifelong Bandit Optimization: No Prior and No Regret](https://mlsanity.com/paper/2210.15513/) (2022)

## Built on by (most cited first, 6 of 6)

- [MaxInfoRL: Boosting exploration in reinforcement learning through information gain maximization](https://mlsanity.com/paper/2412.12098/) (2024)
- [All models are wrong, some are useful: Model Selection with Limited Labels](https://mlsanity.com/paper/2410.13609/) (2024)
- [Symmetric Linear Bandits with Hidden Symmetry](https://mlsanity.com/paper/2405.13899/) (2024)
- [Large Language Model Selection with Limited Annotations](https://mlsanity.com/paper/2605.24981/) (2026)
- [Large Language Model Selection with Limited Annotations](https://mlsanity.com/paper/2510.09418/) (2025)
- [Improved Training Mechanism for Reinforcement Learning via Online Model Selection](https://mlsanity.com/paper/2512.02214/) (2025)

## Abstract (arXiv)

Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online learning algorithms that treat different models as experts. Existing methods, however, scale poorly (polyM) with the number of models M in terms of their regret. Our key insight is that, for model selection in linear bandits, we can emulate full-information feedback to the online learner with a favorable bias-variance trade-off. This allows us to develop ALEXP, which has an exponentially improved (log M) dependence on M for its regret. ALEXP has anytime guarantees on its regret, and neither requires knowledge of the horizon n, nor relies on an initial purely exploratory stage. Our approach utilizes a novel time-uniform analysis of the Lasso, establishing a new connection between online learning and high-dimensional statistics.