# Feature and Parameter Selection in Stochastic Linear Bandits

arXiv: https://arxiv.org/abs/2106.05378 · HTML: https://mlsanity.com/paper/2106.05378/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 13 of 13)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Corralling a Band of Bandit Algorithms](https://mlsanity.com/paper/1612.06246/) (2016)
- [Model Selection in Contextual Stochastic Bandit Problems](https://mlsanity.com/paper/2003.01704/) (2020)
- [Regret Bound Balancing and Elimination for Model Selection in Bandits and RL](https://mlsanity.com/paper/2012.13045/) (2020)
- [Meta-learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2005.08531/) (2020)
- [Latent Bandits Revisited](https://mlsanity.com/paper/2006.08714/) (2020)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Leveraging Good Representations in Linear Contextual Bandits](https://mlsanity.com/paper/2104.03781/) (2021)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [Regret Balancing for Bandit and RL Model Selection](https://mlsanity.com/paper/2006.05491/) (2020)

## Built on by (most cited first, 5 of 5)

- [Anytime Model Selection in Linear Bandits](https://mlsanity.com/paper/2307.12897/) (2023)
- [On the Complexity of Representation Learning in Contextual Linear Bandits](https://mlsanity.com/paper/2212.09429/) (2022)
- [Symmetric Linear Bandits with Hidden Symmetry](https://mlsanity.com/paper/2405.13899/) (2024)
- [EasyFS: an Efficient Model-free Feature Selection Framework via Elastic Transformation of Features](https://mlsanity.com/paper/2402.05954/) (2024)
- [Riemannian Manifold Learning for Stackelberg Games with Neural Flow Representations](https://mlsanity.com/paper/2502.05498/) (2025)

## Abstract (arXiv)

We study two model selection settings in stochastic linear bandits (LB). In the first setting, which we refer to as feature selection, the expected reward of the LB problem is in the linear span of at least one of M feature maps (models). In the second setting, the reward parameter of the LB problem is arbitrarily selected from M models represented as (possibly) overlapping balls in mathbb Rd. However, the agent only has access to misspecified models, i.e.,~estimates of the centers and radii of the balls. We refer to this setting as parameter selection. For each setting, we develop and analyze a computationally efficient algorithm that is based on a reduction from bandits to full-information problems. This allows us to obtain regret bounds that are not worse (up to a √log M factor) than the case where the true model is known. This is the best-reported dependence on the number of models M in these settings. Finally, we empirically show the effectiveness of our algorithms using synthetic and real-world experiments.