We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem several approaches based on the approximation of the objective function by consensus- and kinetic-based particle optimization methods on the search space are developed. In [1], we combine a sample average approximation and a quadrature strategy with consensus-based algorithms, and analyze the resulting methods using a mean-field approximation. Their connection is established, and several numerical experiments show the validity of the proposed algorithms and investigate their rates of convergence. In [2], we combine variable-sample strategies and consensus- and kinetic-based algorithms. More specifically, we introduce a novel variable-sample-inspired time-discrete consensus-type algorithm and demonstrate its enhanced computational efficiency with respect to the methods proposed in [1]. Subsequently, we present an alternative time-continuous kinetic-based description of the algorithm, which allows us to exploit tools of kinetic theory to conduct a comprehensive theoretical analysis. Finally, we test the consistency of the proposed modelling approaches through several numerical experiments. [1] S. Bonandin, M. Herty. Consensus-based algorithms for stochastic optimization problems. Preprint arXiv:2404.10372, 2024. [2] S. Bonandin, M. Herty. Kinetic variable-sample methods for stochastic optimization problems. Preprint arXiv:2502.17982, 2025.