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Coronary CT Angiography (CCTA) is susceptible to various distortions (e.g., artifacts and noise), which severely compromise the exact diagnosis of cardiovascular diseases. The appropriate CCTA Vessel-level Image Quality Assessment (CCTA VIQA) algorithm can be used to reduce the risk of error diagnosis. The primary challenges of CCTA VIQA are that the local part of coronary that determines final quality is hard to locate. To tackle the challenge, we formulate CCTA VIQA as a multiple-instance learning (MIL) problem, and exploit Transformer-based MIL backbone (termed as T-MIL) to aggregate the multiple instances along the coronary centerline into the final quality. However, not all instances are informative for final quality. There are some quality-irrelevant/negative instances intervening the exact quality assessment(e.g., instances covering only background or the coronary in instances is not identifiable). Therefore, we propose a Progressive Reinforcement learning based Instance Discarding module (termed as PRID) to progressively remove quality-irrelevant/negative instances for CCTA VIQA. Based on the above two modules, we propose a Reinforced Transformer Network (RTN) for automatic CCTA VIQA based on end-to-end optimization. Extensive experimental results demonstrate that our proposed method achieves the state-of-the-art performance on the real-world CCTA dataset, exceeding previous MIL methods by a large margin.