Before revision:  We show that the optimization problem can be effectively solved efficiently, yielding an improved partitioned learned Bloom filter , which partitions the score space and utilizes separate backup Bloom filters for each region . Experimental results from both simulated and real-world datasets show significant performance improvements from our optimization approach over both the original learned Bloom filter constructions and previously proposed heuristic improvements.
After revision:  We show that the optimization problem can be effectively solved efficiently, yielding an improved partitioned learned Bloom filter , and using our framework derive algorithms that can achieve near-optimal performance in many cases . Experimental results from both simulated and real-world datasets show significant performance improvements from our optimization approach over both the original learned Bloom filter constructions and previously proposed heuristic improvements.