_{t=0} \left( \sum_u P^{\wh {\bd \gamma}, \bd f}_t(u|x) \wh Q^{\wh {\bd \gamma}, \bd f}_t(x,u) - P(u|x) \wh Q^{\wh {\bd \gamma}, \bd f}_t(x,u)\right) + \sum^T_{t=0} \| f_t \|_{\infty} \| \mu^{\wh {\bd \gamma}, \bd f}_t - \pi^{\wh {\bd \gamma}, \bd f}_t \|_0,\end{aligned}$$ where in the first equality we have used 