Nearly Optimal Best Arm Identification for Semiparametric Bandits

Researcher Seok-Jin Kim has published a breakthrough paper titled 'Nearly Optimal Best Arm Identification for Semiparametric Bandits' that solves a long-standing problem in machine learning decision theory. The work addresses semiparametric bandits, where rewards are linear in known arm features plus an unknown additive baseline shift—a more realistic model than standard linear bandits for many real-world applications like recommendation systems and clinical trials. This setting requires orthogonalized regression and had remained open regarding its instance-optimal sample complexity.

Kim establishes an attainable instance-dependent lower bound for the transductive setting, characterized by linear-bandit complexity on shifted features. He then proposes a computationally efficient phase-elimination algorithm based on a novel XY-design for orthogonalized regression. The analysis yields a nearly optimal high-probability sample-complexity upper bound, up to logarithmic factors and an additive d² term where d represents dimensionality.

Experiments demonstrate clear practical advantages, with the new algorithm outperforming prior baselines on both synthetic instances and the Jester dataset—a real-world joke recommendation dataset commonly used in bandit research. The work, accepted at AISTATS 2026, provides both theoretical guarantees and practical implementation benefits for systems that need to efficiently identify the best option among many while accounting for unknown baseline effects.