>>11389008B&B will not find a solution until the end of the universe unless the problem is so trivial you could manually pinpoint the solution without even using any kind of algorithm. There are a series of problems and open questions related to that which reveal why ML is so good (far beyond the theory). The theory says ML should be at least as good as B&B (except the constant) but only better in restricted cases (see nesterov). That at least puts it squarely as a superior solution but nevermind that for a second.
The first problem with B&B compared to ML is that B&B doesn't give you solutions, it gives you eligible solution spaces. This also means it can't select a really good but not perfect solution, that is outside of one of the regions it has selected. This is the same problem all las vegas methods have and turns the lower bound into a tight bound, hence preventing B&B from ever actually being good.
The second problem is the assumption that you are looking for an optimal solution ("within a tolerance" is merely proportional, it amounts to the same shit).
The third problem is that it cannot operates simultaneously in every dimension, thus it explodes when the problem is non-trivial, to such a degree that it wouldn't be viable for even problems of size ~500-1000, which are really small problems.
As a result, ML can solve combinatorial problems arbitrarily well under some relatively mild regularity assumption in linear time (!). B&B can never do that.
Now, comparing to RL is a lot more realistic. Then, you lose the weakness of the bound under mild assumptions (the bound is the same), but you do retain the mistake that is space partitioning in terms of dimensional explosion (RL does not have this problem) as well as the optimal solution hypothesis (likewise, RL works better in that scenario).
In conclusion, the only reason you should be using straight optimization algorithms is if you don't want a solution, but rather you want to analyse the optima.
