You are right. I didn't phrase it correctly. What is algorithm independent is the theoretical performance bound for a given data complexity. Sure, not all alg

You are right. I didn't phrase it correctly. What is algorithm independent is the theoretical performance bound for a given data complexity. Sure, not all algorithms are the same, but the best performance that can theoretically be achieved with a given iid sample of a given size is algorithm independent. So yes, a better algo can get same performance with less data, but limit stays the same.