Fixed-Budget Best-Arm Identification in Contextual Bandits: A Static-Adaptive Algorithm

We study the problem of best-arm identification (BAI) in contextual bandits in the fixed-budget setting. We propose a general successive elimination algorithm that proceeds in stages and eliminates a fixed fraction of suboptimal arms in each stage. This design takes advantage of the strengths of static and adaptive allocations. We analyze the algorithm in linear models and obtain a better error bound than prior work. We also apply it to generalized linear models (GLMs) and bound its error. This is the first BAI algorithm for GLMs in the fixed-budget setting. Our extensive numerical experiments show that our algorithm outperforms the state of art.