We study a novel variant of the parameterized bandits problem in which the learner can observe auxiliary feedback that is correlated with the observed reward. The auxiliary feedback is readily available in many real-life applications, e.g., an online platform that wants to recommend the best-rated services to its users can observe the user's rating of service (rewards) and collect additional information like service delivery time (auxiliary feedback). We first develop a method that exploits auxiliary feedback to build a reward estimator with tight confidence bounds, leading to a smaller regret. We then characterize the regret reduction in terms of the correlation coefficient between reward and auxiliary feedback. Experimental results in different settings also verify the performance gain achieved by our proposed method.