Decision making models described as problems of multicriterial optimization are very complicated for investigation, because the property of criteria contradictoriness leads to the notion of the solution as the set of non-dominated parameters (Pareto set). The complexity of these problems increases significantly in the case where criteria are multiextremal. In the paper a novel algorithm for multicriterial black-box optimization with multiextremal criteria is considered. This algorithm applies ideas of complexity reduction when the initial multicriterial problem is reduced to a set of univariate scalar subproblems on the base of Peano mapping and maximum convolution. For solving univariate problems an information-statistical global optimization algorithm with guaranteed convergence to global optimum is used. As a core of novelty, this algorithm includes in its computational scheme a machine learning procedure with combination of accumulating the information of solved subproblems that allows one to significantly accelerate building the Pareto set. Effectiveness of the proposed approach is estimated in the representative computational experiment on test sets of multicriterial problems with multiextremal criteria for different dimensions, in comparison with several nature-inspired multiobjective optimization algorithms.