Random Boost is an algorithm I have developed for my master's thesis. The central idea is that Random Boost builds on Gradient Boosted Trees, but adds a new random component to the boosting procedure concerning the depth of a tree. More specifically, at each iteration, a random number between 1 and some upper limit is drawn that determines the maximally possible depth a tree can have at a certain step.
Please note that this algorithm is by no means efficient. Rather consider it as an effective alpha version.