Recent studies have demonstrated that learned Bloom filters, which combine machine learning with the classical Bloom filter, can achieve superior memory efficiency. However, existing learned Bloom filters face two critical unresolved challenges: the balance between the machine learning model size and the Bloom filter size is not optimal, and the reject time cannot be minimized effectively. We propose the Cascaded Learned Bloom Filter (CLBF) to address these issues. Our dynamic programming-based optimization automatically selects configurations that achieve an optimal balance between the model and filter sizes while minimizing reject time. Experiments on real-world datasets show that CLBF reduces memory usage by up to 24% and decreases reject time by up to 14 times compared to state-of-the-art learned Bloom filters.