  We present a novel variant of the multi-level Monte Carlo method that
effectively utilizes a reserved computational budget on a high-performance
computing system to minimize the mean squared error. Our approach combines
concepts of the continuation multi-level Monte Carlo method with dynamic
programming techniques following Bellman's optimality principle, and a new
parallelization strategy based on a single distributed data structure.
Additionally, we establish a theoretical bound on the error reduction on a
parallel computing cluster and provide empirical evidence that the proposed
method adheres to this bound. We implement, test, and benchmark the approach on
computationally demanding problems, focusing on its application to acoustic
wave propagation in high-dimensional random media.
