Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises

We present stochastic consensus and convergence of the discrete consensus-based optimization (CBO) algorithm with random batch interactions heterogeneous external noises. Despite wide applications successful performance in many practical simulations, CBO was not rigorously investigated such a generality. In this work, we introduce generalized weighted representative point interactions, show that proposed exhibits toward common equilibrium state exponentially fast under suitable assumptions on system parameters. For this, recast given as model switching network topology, then use mixing property over sufficiently long time interval to derive estimates mean square almost sure senses. Our analysis significantly improves earlier works models full homogeneous