Studies adaptive routing of prompts across multiple LLM “experts” to maximize response quality under limited feedback, formulated as a K-armed contextual bandit over a T-round horizon with a feedback budget m much smaller than T. Proposes algorithms achieving regret of O(dT/sqrt(m)) in the full-information setting and O(dT*sqrt(K)/m) in the bandit setting. Includes theoretical regret bounds alongside experimental validation.
