However, you are mathematically wrong. Doing things the way you describe is another form of A/B testing, just one designed to reduce the regret incurred during the test. You still get the linear growth in regret I described (i.e., there is some % chance you picked the wrong branch, and you are leaving money on the table forever after).
Of course, your way is also economically correct, and the theoretical CS guys are wrong. They shouldn't be trying to minimize regret, they should be minimizing time discounted regret.
(Yes, I'm being extremely pedantic. I'm a mathematician, it comes with the territory.)
A guess at good strategy in those situations would be something that enables you to choose a good path from a small number of options and keep doing so - on the basis that the cumulative advantage will be far more important than any particular choice in itself. Sounds like A/B testing would win if you could actually map the complexity of the problem correctly.