Earlier quoted context omitted.
Isn't A/B testing pretty much going to behave like a steepest ascent hill climbing? At each micro decision point you take what looks like the 'best' option but that means you can get stuck in local maxima?
This is interesting but I don't think I fully understand. Do you mind dumbing it down for me?
However, it turns out the heavy traffic at the other A branch was just for a few miles and then it was actually empty after that --- you took optimum local decisions at each step but since you weren't able to look at the big picture, you didn't actually choose the globally optimal route.
As others have pointed, this is related to the mathematical concepts of local and global maxima: sometimes your optimization algorithm happily stops when it finds a local maximum, ignoring the much better global maximum because it didn't actually traversed the whole search domain.