 get $$\begin{aligned} & \sup_{P \in \cM(\sU | \sX)} \sum_x \pi_P(x) \left[\sum^{T-0}_{t=0} \left( \sum_u P^{\wh {\bd \gamma}, \bd f}_t(u|x) \wh Q^{\wh {\bd \gamma}, \bd f}_t(x,u) \right) + \sum_u P^{\wh {\bd \gamma}, \bd f}_T(u|x) \wh Q^{\wh {\bd \gamma}, \bd f}_T(x,u)