  In 1985, for detecting a change in distribution, Pollak introduced a specific
minimax performance metric and a randomized version of the Shiryaev-Roberts
procedure where the zero initial condition is replaced by a random variable
sampled from the quasi-stationary distribution of the Shiryaev-Roberts
statistic. Pollak proved that this procedure is third-order asymptotically
optimal as the mean time to false alarm becomes large. The question of whether
Pollak's procedure is strictly minimax for any false alarm rate has been open
for more than two decades, and there were several attempts to prove this strict
optimality. In this paper, we provide a counterexample which shows that
Pollak's procedure is not optimal and that there is a strictly optimal
procedure which is nothing but the Shiryaev-Roberts procedure that starts with
a specially designed deterministic point.
