Hesitant adaptive search: the distribution of the number of iterations to convergence

Hesitant adaptive search is a stochastic optimisation procedure which accom modates hesitation, or pausing, at objective function values. It lies betwe en pure adaptive starch (which strictly improves at each iteration) and sim ulated annealing with constant temperature (which allows backtracking, or t he acceptance of worse function values). In this paper we build on an earli er work and make two contributions; first, we link hesitant adaptive search to standard counting process theory, and second, we use this to derive the exact distribution of the number of iterations of hesitant adaptive search to termination.