  Consensus-based optimization (CBO) is a versatile multi-particle
metaheuristic optimization method suitable for performing nonconvex and
nonsmooth global optimizations in high dimensions. It has proven effective in
various applications while at the same time being amenable to a theoretical
convergence analysis. In this paper, we explore a variant of CBO, which
incorporates truncated noise in order to enhance the well-behavedness of the
statistics of the law of the dynamics. By introducing this additional
truncation in the noise term of the CBO dynamics, we achieve that, in contrast
to the original version, higher moments of the law of the particle system can
be effectively bounded. As a result, our proposed variant exhibits enhanced
convergence performance, allowing in particular for wider flexibility in
choosing the noise parameter of the method as we confirm experimentally. By
analyzing the time-evolution of the Wasserstein-$2$ distance between the
empirical measure of the interacting particle system and the global minimizer
of the objective function, we rigorously prove convergence in expectation of
the proposed CBO variant requiring only minimal assumptions on the objective
function and on the initialization. Numerical evidences demonstrate the benefit
of truncating the noise in CBO.
