Existing state-of-the-art dense object detection techniques tend to produce a large number of false positive detections on difficult images with complex scenes because they focus on ensuring a high recall. To improve the detection accuracy, we propose an Adaptive Important Region Selection (AIRS) framework guided by Evidential Q-learning coupled with a uniquely designed reward function. Inspired by human visual attention, our detection model conducts object search in a top-down, hierarchical fashion. It starts from the top of the hierarchy with the coarsest granularity and then identifies the potential patches likely to contain objects of interest. It then discards non-informative patches and progressively moves downward on the selected ones for a fine-grained search. The proposed evidential Q-learning systematically encodes epistemic uncertainty in its evidential-Q value to encourage the exploration of unknown patches, especially in the early phase of model training. In this way, the proposed model dynamically balances exploration-exploitation to cover both highly valuable and informative patches. Theoretical analysis and extensive experiments on multiple datasets demonstrate that our proposed framework outperforms the SOTA models.