>eventually the two systems will tend towards showing the improved recommendations, and the lift will tend towards zero
While this is probably true in many realistic cases, I'm skeptical on theoretical grounds.
Suppose the replacement algorithm happens to be run on a quantum computer. When you search for a book such as "I wish I knew a prime factor of 132,200,813,987,918,309", it near-instantly recommends you might be interested in the book "Interesting facts about 373,587,911".
If P!=NP and the original system is running on conventional hardware, there's no way it can match the replacement.
While this is probably true in many realistic cases, I'm skeptical on theoretical grounds.
Suppose the replacement algorithm happens to be run on a quantum computer. When you search for a book such as "I wish I knew a prime factor of 132,200,813,987,918,309", it near-instantly recommends you might be interested in the book "Interesting facts about 373,587,911".
If P!=NP and the original system is running on conventional hardware, there's no way it can match the replacement.