Thompson sampling
Discovered in 1933. Popularized in 2010.
Simple schoolbook A/B testing example: pick which of 2 websites to show a visitor, using a coin flip… in other words, draw from a Bernoulli distribution to decide which site to show.
Thompson uses a beta distribution to weight how often to show the one or the other version of the website to customers. The beta dist has 2 parameters, α and β. Here these parameters represent prior successes and fails (wins and losses), by count. We must of course define what win and fail mean, e.g. when visitor clicks the buy button it's a win, else a fail.
Going about things with Thompson sampling you win a lot of efficiency, your company doesn't lose much revenue while you're running the A/B experiment, since the one shown to work better is quickly shown more often.