# New Insights into Bootstrapping for Bandits

arXiv: https://arxiv.org/abs/1805.09793 · HTML: https://mlsanity.com/paper/1805.09793/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

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

- [Diffusion Approximations for Thompson Sampling in the Small Gap Regime](https://mlsanity.com/paper/2105.09232/) (2021)
- [Residual Bootstrap Exploration for Stochastic Linear Bandit](https://mlsanity.com/paper/2202.11474/) (2022)
- [Debiasing Samples from Online Learning Using Bootstrap](https://mlsanity.com/paper/2108.00236/) (2021)
- [Multiplier Bootstrap-based Exploration](https://mlsanity.com/paper/2302.01543/) (2023)
- [CORe: Capitalizing On Rewards in Bandit Exploration](https://mlsanity.com/paper/2103.04387/) (2021)
- [GuideBoot: Guided Bootstrap for Deep Contextual Bandits](https://mlsanity.com/paper/2107.08383/) (2021)

## Abstract (arXiv)

We investigate the use of bootstrapping in the bandit setting. We first show that the commonly used non-parametric bootstrapping (NPB) procedure can be provably inefficient and establish a near-linear lower bound on the regret incurred by it under the bandit model with Bernoulli rewards. We show that NPB with an appropriate amount of forced exploration can result in sub-linear albeit sub-optimal regret. As an alternative to NPB, we propose a weighted bootstrapping (WB) procedure. For Bernoulli rewards, WB with multiplicative exponential weights is mathematically equivalent to Thompson sampling (TS) and results in near-optimal regret bounds. Similarly, in the bandit setting with Gaussian rewards, we show that WB with additive Gaussian weights achieves near-optimal regret. Beyond these special cases, we show that WB leads to better empirical performance than TS for several reward distributions bounded on [0,1]. For the contextual bandit setting, we give practical guidelines that make bootstrapping simple and efficient to implement and result in good empirical performance on real-world datasets.