# Experimental Design for Semiparametric Bandits

arXiv: https://arxiv.org/abs/2506.13390 · HTML: https://mlsanity.com/paper/2506.13390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 21 of 21)

- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits](https://mlsanity.com/paper/1904.00242/) (2019)
- [Fully adaptive algorithm for pure exploration in linear bandits](https://mlsanity.com/paper/1710.05552/) (2017)
- [Instance-Dependent Near-Optimal Policy Identification in Linear MDPs via Online Experiment Design](https://mlsanity.com/paper/2207.02575/) (2022)
- [Minimax Optimal Fixed-Budget Best Arm Identification in Linear Bandits](https://mlsanity.com/paper/2105.13017/) (2021)
- [Action Centered Contextual Bandits](https://mlsanity.com/paper/1711.03596/) (2017)
- [Doubly robust Thompson sampling for linear payoffs](https://mlsanity.com/paper/2102.01229/) (2021)
- [Minimax Optimal Algorithms for Fixed-Budget Best Arm Identification](https://mlsanity.com/paper/2206.04646/) (2022)
- [PAC-Bayesian Offline Contextual Bandits With Guarantees](https://mlsanity.com/paper/2210.13132/) (2022)
- [Semiparametric Contextual Bandits](https://mlsanity.com/paper/1803.04204/) (2018)
- [Best Arm Identification in Generalized Linear Bandits](https://mlsanity.com/paper/1905.08224/) (2019)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Instance-optimal PAC Algorithms for Contextual Bandits](https://mlsanity.com/paper/2207.02357/) (2022)
- [PAC Identification of Many Good Arms in Stochastic Multi-Armed Bandits](https://mlsanity.com/paper/1901.08386/) (2019)
- [Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift](https://mlsanity.com/paper/2311.15961/) (2023)
- [Contextual Multi-armed Bandit Algorithm for Semiparametric Reward Model](https://mlsanity.com/paper/1901.11221/) (2019)
- [Semi-Parametric Contextual Bandits with Graph-Laplacian Regularization](https://mlsanity.com/paper/2205.08295/) (2022)
- [GBOSE: Generalized Bandit Orthogonalized Semiparametric Estimation](https://mlsanity.com/paper/2301.08781/) (2023)

## Built on by (most cited first, 1 of 1)

- [Nearly Optimal Best Arm Identification for Semiparametric Bandits](https://mlsanity.com/paper/2604.03969/) (2026)

## Abstract (arXiv)

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in practice. We propose the first experimental-design approach that simultaneously offers a sharp regret bound, a PAC bound, and a best-arm identification guarantee. Our method attains the minimax regret tildeO(√dT), matching the known lower bound for finite-armed linear bandits, and further achieves logarithmic regret under a positive suboptimality gap condition. These guarantees follow from our refined non-asymptotic analysis of orthogonalized regression that attains the optimal √d rate, paving the way for robust and efficient learning across a broad class of semiparametric bandit problems.