強化学習輪読 #11 - Qiita

\begin{aligned} G_{t}-V\left(S_{t}\right) &=R_{t+1}+\gamma G_{t+1}-V\left(S_{t}\right)+\gamma V\left(S_{t+1}\right)-\gamma V\left(S_{t+1}\right) \\ &=\delta_{t}+\gamma\left(G_{t+1}-V\left(S_{t+1}\right)\right) \\ &=\delta_{t}+\gamma \delta_{t+1}+\gamma^{2}\left(G_{t+2}-V\left(S_{t+2}\right)\right) \\ &=\delta_{t}+\gamma \delta_{t+1}+\gamma^{2} \delta_{t+2}+\cdots+\gamma^{T-t-1} \delta_{T-1}+\gamma