A simplified run time analysis of the univariate marginal distribution algorithm on LeadingOnes

With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing LeadingOnes benchmark function in desirable regime with low genetic drift. If population size is at least quasilinear, then, high probability, UMDA samples optimum number of iterations that linear problem divided by logarithm UMDA's selection rate. This improves over previous guarantee, obtained Dang and Lehre (2015) via deep level-based method, both terms demonstrating further gains from small rates. Under similar assumptions, lower bound matches our upper up to constant factors.