Comparison-based algorithms: worst-case optimality, optimality w.r.t a bayesian prior, the intraclass-variance minimization in EDA, and implementations with billiards
Sylvain Gelly, Sylvie Ruette and Olivier Teytaud
In: PPSN-BTP-Workshop, 10th International Conference on Parallel Problem Solving from Nature (PPSN 2006), 9-13 Sep 2006, Reykjavik.
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-p oints by the way of billiard algorithms.