Abstract: This paper is centered on the analysis of comparison-based algorithms. It has been shown recently that these algorithms are at most linearly convergent with a constant 1 − O(1/d); we here show that these algorithms are however optimal for robust optimization w.r.t increasing transformations of the fitness. We then turn our attention to the design of optimal comparison-based algorithms. No-Free-Lunch theorems have shown that introducing priors is necessary in order to design algorithms better than others; therefore, we include a bayesian prior in the spirit of learning theory. We show that these algorithms have a nice interpretation in terms of Estimation-Of-Distribution algorithms, and provide tools for the optimal design of generations of lambda-points by the way of billiard algorithms.