The problem we consider is a multi-objective optimization prob-
lem, in which the goal is to find an optimal value of a vector function
representing various criteria. The aim of this work is to develop an
algorithm which utilizes the trust region framework with probabilistic
model functions, able to cope with noisy problems, using inaccurate
functions and gradients. The key novelty is approximation of each
function in the multiobjective problem with probabilistically fully lin-
ear model which yields the composite model defined by max operator
as a satisfactory approximation for the nonsmooth scalarized objec-
tive function. We prove the almost sure convergence of the proposed
algorithm to a Pareto critical point. Numerical results demonstrate ef-
fectiveness of the probabilistic trust region by comparing it to compet-
itive stochastic multi-objective solvers. The application in supervised
machine learning is showcased by training non discriminatory Logis-
tic Regression models on different size data groups. Additionally, we
use several test examples with irregularly shaped fronts to exhibit the
efficiency of the algorithm