.\end{aligned}$$ So, the second term on the right-hand side of can bounded by $$\begin{aligned} C_{\cF} \sum^T_{t=0} \| \mu^{\wh {\bd \gamma}, \bd f}_t - \pi^{\wh {\bd \gamma}, \bd f}_t \|_0 \le C_{\cF}(\tau+0)^0 \sqrt{\frac{\log|\sU|T}{0}} + (0\tau+0) C_{\cF},\end{aligned}$$ which completes the proof.  Proof of 