   \E^{\wh{\bd{\gamma}},\bd{f}}_x\left[\sum^T_{t=0}f_t(X_t,U_t) - \Psi(\bd{f})\right] &\le \sup_{P \in \cM(\sU|\sX)}\sum_{x}\pi_P(x) \wh{W}_{x,0} + C_\cF  \sum^T_{t=0} \| \mu^{\wh{\bd{\gamma}},\bd{f}}_t - \pi^{\wh{\bd{\gamma}},\bd{f}}_t \|_0