The paper introduces ID‑TAP, an information‑directed dueling‑bandit framework for test‑time personalization of large language model agents across large discrete persona spaces. ID‑TAP couples a query‑conditioned neural utility model that learns per‑query scores while sharing statistical strength across queries with a lightweight Bradley‑Terry explorer that selects challenger–challenge pairs through binary comparisons. Comparison evidence is transferred across queries via similarity‑weighted warm‑start initialization, enabling efficient updates of challenger scores and preserving query‑specific utility. The framework is scalable to large discrete persona sets, as the neural model shares statistical strength across queries while preserving per‑query specificity, and the Bradley‑Terry updates are computed efficiently, allowing rapid adaptation within the ten‑round comparison budget. The method is evaluated on seven user‑conditioned generation benchmarks under both reference‑based and model‑based preference simulators, using a fixed ten‑round comparison budget per query. Across all settings, ID‑TAP attains the highest aggregate performance among the evaluated baselines, demonstrating that information‑directed challenger selection effectively bridges exploration and persona adaptation for test‑time agent personalization.