In this work, we study multi-source test-time model adaptation from user feedback, where $K$ distinct models are established for adaptation. To allow efficient adaptation, we cast the problem as a stochastic decision-making process, aiming to determine the best adapted model after adaptation. We discuss two frameworks: multi-armed bandit learning and multi-armed dueling bandits. Compared to multi-armed bandit learning, the dueling framework allows pairwise collaboration among $K$ models, which is solved by a novel method named Co-UCB proposed in this work. Experiments on six datasets of extractive question answering (QA) show that the dueling framework using Co-UCB is more effective than other strong baselines for our studied problem.