Robust Best-arm Identification in Linear Bandits
Wei Wang Sattar Vakili Ilija Bogunovic
We study the robust best-arm identification problem (RBAI) in the case of
linear rewards. The primary objective is to identify a near-optimal robust arm,
which involves selecting arms at every round and assessing their robustness by
exploring potential adversarial actions. This approach is particularly relevant
when utilizing a simulator and seeking to identify a robust solution for
real-world transfer. To this end, we present an instance-dependent lower bound
for the robust best-arm identification problem with linear rewards.
Furthermore, we propose both static and adaptive bandit algorithms that achieve
sample complexity that matches the lower bound. In synthetic experiments, our
algorithms effectively identify the best robust arm and perform similarly to
the oracle strategy. As an application, we examine diabetes care and the
process of learning insulin dose recommendations that are robust with respect
to inaccuracies in standard calculators. Our algorithms prove to be effective
in identifying robust dosage values across various age ranges of patients.