Experimental Design for Semiparametric Bandits

TL;DR

This paper introduces a novel experimental-design method for semiparametric bandits that achieves optimal regret bounds, including minimax and logarithmic regret, by refining non-asymptotic analysis of orthogonalized regression.

Contribution

It presents the first approach combining sharp regret, PAC, and best-arm guarantees for semiparametric bandits, generalizing classical linear bandit methods.

Findings

Attains minimax regret $ ilde{O}( ext{sqrt}(dT))$ matching lower bounds.

Achieves logarithmic regret under positive suboptimality gap.

Provides refined non-asymptotic analysis of orthogonalized regression.

Abstract

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.