Guidelines for transthoracic echocardiographic examination recommend the acquisition of multiple video clips from different views of the heart, resulting in a large number of clips. Typically, automated methods, for instance, disease classifiers, either use one clip or average predictions from all clips. Relying on one clip ignores complementary information available from other clips, while using all clips is computationally expensive and may be prohibitive for clinical adoption. To select the optimal subset of clips that maximize performance for a specific task (image-based disease classification), we propose a method optimized through reinforcement learning. In our method, an agent learns to either keep processing view-specific clips to reduce the disease classification uncertainty or stop processing if the achieved classification confidence is sufficient. Furthermore, we propose a learnable attention-based aggregation method as a flexible way of fusing information from multiple clips. The proposed method obtains an AUC of 0.91 on the task of detecting cardiac amyloidosis using only 30% of all clips, exceeding the performance achieved from using all clips and from other benchmarks.