# Experimental Design for Regret Minimization in Linear Bandits

arXiv: https://arxiv.org/abs/2011.00576 · HTML: https://mlsanity.com/paper/2011.00576/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2020.

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

- [High-Dimensional Experimental Design and Kernel Bandits](https://mlsanity.com/paper/2105.05806/) (2021)
- [Contextual Bandits with Large Action Spaces: Made Practical](https://mlsanity.com/paper/2207.05836/) (2022)
- [A Fully Problem-Dependent Regret Lower Bound for Finite-Horizon MDPs](https://mlsanity.com/paper/2106.13013/) (2021)
- [Pareto Optimal Model Selection in Linear Bandits](https://mlsanity.com/paper/2102.06593/) (2021)
- [Dealing With Misspecification In Fixed-Confidence Linear Top-m Identification](https://mlsanity.com/paper/2111.01479/) (2021)
- [An Experimental Design Approach for Regret Minimization in Logistic Bandits](https://mlsanity.com/paper/2202.02407/) (2022)
- [The price of unfairness in linear bandits with biased feedback](https://mlsanity.com/paper/2203.09784/) (2022)
- [Augmenting Online RL with Offline Data is All You Need: A Unified Hybrid RL Algorithm Design and Analysis](https://mlsanity.com/paper/2505.13768/) (2025)
- [Spectral learning of Bernoulli linear dynamical systems models](https://mlsanity.com/paper/2303.02060/) (2023)
- [Efficient and Interpretable Bandit Algorithms](https://mlsanity.com/paper/2310.14751/) (2023)
- [Minimax Optimal Regret for Causal Logistic Bandits with Counterfactual Fairness](https://mlsanity.com/paper/2610.01377/) (2026)

## Abstract (arXiv)

In this paper we propose a novel experimental design-based algorithm to minimize regret in online stochastic linear and combinatorial bandits. While existing literature tends to focus on optimism-based algorithms--which have been shown to be suboptimal in many cases--our approach carefully plans which action to take by balancing the tradeoff between information gain and reward, overcoming the failures of optimism. In addition, we leverage tools from the theory of suprema of empirical processes to obtain regret guarantees that scale with the Gaussian width of the action set, avoiding wasteful union bounds. We provide state-of-the-art finite time regret guarantees and show that our algorithm can be applied in both the bandit and semi-bandit feedback regime. In the combinatorial semi-bandit setting, we show that our algorithm is computationally efficient and relies only on calls to a linear maximization oracle. In addition, we show that with slight modification our algorithm can be used for pure exploration, obtaining state-of-the-art pure exploration guarantees in the semi-bandit setting. Finally, we provide, to the best of our knowledge, the first example where optimism fails in the semi-bandit regime, and show that in this setting our algorithm succeeds.