diff --git a/docs/errata.md b/docs/errata.md index e0330ce..8b18b44 100644 --- a/docs/errata.md +++ b/docs/errata.md @@ -17,3 +17,18 @@ G_8=r_9+\gamma G_9=-1+0.6 \times(-2.176)=-2.3056 \approx-2.3 \end{array} $$ +* 149页,式(6.15) 改为 + +$$ +\begin{aligned} +V^{\pi}(s) &\le Q^{\pi}(s,\pi'(s)) \\ +&=E\left[r_{t}+V^{\pi}\left(s_{t+1}\right) | s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right]\\ +&\le E\left[r_{t}+Q^{\pi}\left(s_{t+1}, \pi^{\prime}\left(s_{t+1}\right)\right) | s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right] \\ +&=E\left[r_{t}+r_{t+1}+V^{\pi}\left(s_{t+2}\right) |s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right] \\ +& \le E\left[r_{t}+r_{t+1}+Q^{\pi}\left(s_{t+2},\pi'(s_{t+2}\right) | s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right] \\ +& = E\left[r_{t}+r_{t+1}+r_{t+2}+V^{\pi}\left(s_{t+3}\right) |s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right] \\ +& \le \cdots\\ +& \le E\left[r_{t}+r_{t+1}+r_{t+2}+\cdots | s_{t}=s, a_{t}=\pi^{\prime}\left(s_{t}\right)\right] \\ +& = V^{\pi'}(s) +\end{aligned} +$$