  The paper is devoted to a stochastic optimal control problem for a two scale,
infinite dimensional, stochastic system. The state of the system consists of
slow and fast component and its evolution is driven by both continuous Wiener
noises and discontinuous Poisson-type noises. The presence of discontinuous
noises is the main feature of the present work. We use the theory of backward
stochastic differential equations (BSDEs) to prove that, as the speed of the
fast component diverges, the value function of the control problem converges to
the solution of a reduced forward backward system that, in turn, is related to
a reduced stochastic optimal control problem.
