Nearly Optimal Best Arm Identification for Semiparametric Bandits
We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $XY$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log f...
| Authors | Seok-Jin Kim |
|---|---|
| Primary category | stat.ML |
| Published | 5 April 2026 |
| Last updated at source | 5 April 2026 |
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