Experimental Design for Semiparametric Bandits

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 $\tilde{O}(\sqrt{dT})$, 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 $\sqrt{d}$ rate, paving the way for robust and efficient learning across a broad class of semiparametric bandit problems.

@article{kim2025_2506.13390,
  title={ Experimental Design for Semiparametric Bandits },
  author={ Seok-Jin Kim and Gi-Soo Kim and Min-hwan Oh },
  journal={arXiv preprint arXiv:2506.13390},
  year={ 2025 }
}