  In order to describe or estimate different quantities related to a specific
random variable, it is of prime interest to numerically generate such a
variate. In specific situations, the exact generation of random variables might
be either momentarily unavailable or too expensive in terms of computation
time. It therefore needs to be replaced by an approximation procedure. As was
previously the case, the ambitious exact simulation of exit times for diffusion
processes was unreachable though it concerns many applications in different
fields like mathematical finance, neuroscience or reliability. The usual way to
describe exit times was to use discretization schemes, that are of course
approximation procedures. Recently, Herrmann and Zucca \cite{Herrmann-Zucca-2}
proposed a new algorithm, the so-called GDET-algorithm (General Diffusion Exit
Time), which permits to simulate exactly the exit time for one-dimensional
diffusions. The only drawback of exact simulation methods using an
acceptance-rejection sampling is their time consumption. In this paper the
authors highlight an acceleration procedure for the GDET-algorithm based on a
multi-armed bandit model. The efficiency of this acceleration is pointed out
through numerical examples.
