Problem Demo

Equations in list

Equivalent Expressions

Not sure why a scroll bar appears here

Metric	Expression 1	Expression 2	Expression 3
\(\bar{v}_{\pi}\)	\(\displaystyle \sum_{s \in S} d(s) v_{\pi}(s)\)	\(\mathbb{E}[v_{\pi}(S)]\)	\(\displaystyle \lim_{n\to\infty} \mathbb{E}[\sum_{t=0}^{n}\gamma^t R_{t+1}]\)
\(\bar{r}_{\pi}\)	\(\displaystyle \sum_{s \in S} d_{\pi}(s) r_{\pi}(s)\)	\(\mathbb{E}[r_{\pi}(S)]\)	\(\displaystyle \textcolor{red}{\lim_{n\to\infty} \frac{1}{n}\mathbb{E}[\sum_{t=0}^{n-1} R_{t+1}]}\)

A temporary work-around is by adding a new (empty) line in the table

Metric	Expression 1	Expression 2	Expression 3
\(\bar{v}_{\pi}\)	\(\displaystyle \sum_{s \in S} d(s) v_{\pi}(s)\)	\(\mathbb{E}[v_{\pi}(S)]\)	\(\displaystyle \lim_{n\to\infty} \mathbb{E}[\sum_{t=0}^{n}\gamma^t R_{t+1}]\)
\(\bar{r}_{\pi}\)	\(\displaystyle \sum_{s \in S} d_{\pi}(s) r_{\pi}(s)\)	\(\mathbb{E}[r_{\pi}(S)]\)	\(\displaystyle \textcolor{red}{\lim_{n\to\infty} \frac{1}{n}\mathbb{E}[\sum_{t=0}^{n-1} R_{t+1}]}\)

Multiple Alignments

When aligning equations at multiple locations, the alignment location for the “Truncated Policy Iteration” is not correct. I’m not sure this should be a problem with MathJax. I’ll report it in the MathJax repo if so.

\[\begin{alignat}{2} v_{\pi 1}^{(0)} &= v_0 \nonumber\\ v_{\pi 1}^{(1)} &= r_{\pi 1} + \gamma P_{\pi 1} v_{\pi 1}^{(0)} &\longrightarrow v_1 \longrightarrow \text{Value Iteration} \nonumber\\ v_{\pi 1}^{(2)} &= r_{\pi 1} + \gamma P_{\pi 1} v_{\pi 1}^{(1)} \nonumber\\ \vdots \nonumber\\ v_{\pi 1}^{(j)} &= r_{\pi 1} + \gamma P_{\pi 1} v_{\pi 1}^{(j-1)} &\longrightarrow \bar{v_1} \longrightarrow \text{Truncated Policy Iteration} \nonumber\\ \vdots \nonumber\\ v_{\pi 1}^{(\infty)} &= r_{\pi 1} + \gamma P_{\pi 1} v_{\pi 1}^{(\infty)} &\longrightarrow v_{\pi 1} \longrightarrow \text{Policy Iteration} \nonumber \end{alignat}\]

Code Block Grammar Check

I wonder where the grammar check for code block was enabled. Here are two examples:

The first one is from my post for equation template/reminder. I have open a topic in discussion, but no one has replied yet. The first one is particularly strange because some part of the eqation becase italic in light mode. When in dark mode, colors are also applied incorrectly to some part of the text but italic text are longer there. I believe this is related to the switch between light and dark theme.

<Mandatory Blank Line>
$$
\begin{align}
D_{KL}(P^*(y|x_i)\ ||\ P(y|x_i; \Theta)) 
    &= \sum_{y} P^*(y|x_i) log \frac{P^*(y|x_i)}{P(y|x_i; \Theta)} \\
    &= \sum_{y} P^*(y|x_i)[logP^*(y|x_i) - logP(y|x_i; \Theta)] \\
    &= \sum_{y} P^*(y|x_i)logP^*(y|x_i) - \sum_{y} P^*(y|x_i)logP(y|x_i; \Theta)
\end{align}
$$
<Mandatory Blank Line>

Another example came from a note about python, the problematic part was an output from Python console. Not sure why it was highlighted in red.

def learn_kwargs(**kwargs):
    print(kwargs)
    print(type(kwargs))
    for key, val in kwargs.items():
        print(f"{key} -> {val}")

>>> learn_kwargs(first_name='Zheng', last_name='Yuan')
{'first_name': 'Zheng', 'last_name': 'Yuan'}
<class 'dict'>
first_name -> Zheng
last_name -> Yuan