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Update codes
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ZhiqingXiao committed Dec 17, 2023
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4 changes: 2 additions & 2 deletions zh2023/errata/202307.md
Original file line number Diff line number Diff line change
Expand Up @@ -283,13 +283,13 @@ $d_ \rm{TV}\left(\rho_ {\pi'}\left(\cdot,\cdot\right)\middle\|\rho_ {\pi''}\left

$=\sum\limits_ {\mathsfit{s'},\tilde r}{\tilde p\left(\mathsfit{s'},\tilde r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[\tilde r+\gamma{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$

$=\sum\limits_ {\mathsfit{s'},r}{p\left(\mathsfit{s'},r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[r-{{\bar r}_ \pi}+\gamma{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$
$=\sum\limits_ {\mathsfit{s'},r}{p\left(\mathsfit{s'},r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[r-{\bar r}_ \pi+\gamma{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$

#### 改为

$=\sum\limits_ {\mathsfit{s'},\tilde r}{\tilde p\left(\mathsfit{s'},\tilde r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[\tilde r+{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$

$=\sum\limits_ {\mathsfit{s'},r}{p\left(\mathsfit{s'},r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[r-{{\bar r}_ \pi}+{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$
$=\sum\limits_ {\mathsfit{s'},r}{p\left(\mathsfit{s'},r\middle\vert\mathsfit{s},\mathsfit{a}\right)\left[r-{\bar r}_ \pi+{\tilde v}_ \pi\left(\mathsfit{s'}\right)\right]}$


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