A popular regret minimization search-or-exploit technique is the Upper Confidence Bound algorithm. Any with statistics backgrounds will be able to make a pretty good guess how it works, but if applied intuitively, 'it can be summed up by the principle of optimism in the face of uncertainty.' (https://jeremykun.com/2013/10/28/optimism-in-the-face-of-uncertainty-the-ucb1-algorithm/).
