常用LaTex语法

常用LaTex语法

• 符号

点	\(\cdot\)	\(\cdots\)	\(\vdots\)	\(\ddots\)
LaTex	\cdot	\cdots	\vdots	\ddots

|等号|\(\approx\)|\(\sim\)|\(\propto\)|\(\geq\)|\(\leq\)|
|--|--|--|--|--|--|--|--|--|--|--|
| LaTex |\approx|\sim|\propto|\geq|\leq|

|箭头|\(\Rightarrow\)|\(\Longrightarrow\)|\(\rightrightarrows\)|\(\rightleftarrows\)|\(\nearrow\)|\(\searrow\)|
|--|--|--|--|--|--|--|--|--|--|--|
| LaTex |\Rightarrow |\Longrightarrow|\rightrightarrows|\rightleftarrows|\nearrow|\searrow|

|运算符| \(\prod\) | \(\sum\)|\(\int\)|\(\partial x\)|\(\nabla\) |\(\in\)|\(\not\in\)|\(\subset\) |\(\not\subset\)|
|--|--|--|--|--|--|--|--|--|--|--|--|--|
| LaTex |\prod |\sum |\int|\partial x|\nabla|\in|\not\in|\subset|\not\subset|

|四则运算|\(a \cdot b\)|\(a \times b\)|\(a \div b\)|\(\frac{a}{b}\)
|--|--|--|--|--|--|--|--|--|--|
| LaTex |a \cdot b|a \times b|a \div b|\frac{a}{b}|

|上/下划线| \(\widetilde x\) | \(\overline{\text{x}}\)|\(\widetilde x\) |\(\tilde x\)|\(\underline{V}_{n}\)|\(\overline V_n\)|
|--|--|--|--|--|--|--|--|--|--|
| LaTex |\widetilde x|\overline{\text{x}}|\widetilde x|\tilde x|\underline{V}{n}|\overline{V}|

|绝对值/取整| \(\vert\) | \(\Vert\)|\(\lfloor\)|\(\rfloor\)|\(\lceil\)|\(\rceil\)
|--|--|--|--|--|--|--|--|--|--|
| LaTex |\vert|\Vert|\lfloor|\rfloor|\lceil|\rceil|

• 字母

字母	\(\mathbb{T}\)	\(\mathcal{T}\)	\(\mathscr{T}\)	\(\mathsf{T}\)	\(\mathtt{T}\)	\(\mathit{T}\)
LaTex	\mathbb	\mathcal	\mathscr	\mathsf	\mathtt	\mathit

希腊字母	\(\zeta\)	\(\eta\)	\(\xi\)	\(\upsilon\)	\(\phi\)	\(\varphi\)	\(\psi\)	\(\omega\)
LaTex	\zeta	\eta	\xi	\upsilon	\phi	\varphi	\psi	\omega

• 公式

\[\pi^*(a|s)= \left\{\begin{array}{l} 1,if \quad a=\arg\max\limits_{a \in A}q^*(s,a)\\ 0,otherwise \end{array}\right. \]

$$
\pi^*(a|s)=
\left\{\begin{array}{l}
1,if \quad a=\arg\max\limits_{a \in A}q^*(s,a)\\
0,otherwise
\end{array}\right.
$$

\[T=\begin{pmatrix} 0 & 0 & 1 & \frac{1}{2} \\ \frac{1}{3} & 0 & 0 & 0 \\ \frac{1}{3} & \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{1}{3} & \frac{1}{2} & 0 & 0 \end{pmatrix} \]

$$
T=\begin{pmatrix}
    0           &           0 & 1 & \frac{1}{2} \\
    \frac{1}{3} &           0 & 0 & 0           \\
    \frac{1}{3} & \frac{1}{2} & 0 & \frac{1}{2} \\
    \frac{1}{3} & \frac{1}{2} & 0 & 0
\end{pmatrix}
$$

\[\begin{array}{l} q_\pi(s,a) \overset{.}{=} E_\pi[G_t|S_t=s,A_t=a] \\ \qquad \quad \ = E_\pi[R_{t+1}+\gamma G_{t+1}|S_t=s,A_t=a] \\ \qquad \quad \ = \sum_{s^\prime,r}p(s^\prime,r|s,a)[r+\gamma \sum_{a^\prime}\pi(a^\prime|s^\prime)E_\pi[G_{t+1}|S_{t+1}=s^\prime,A_{t+1}=a^\prime]] \\ \qquad \quad \ = \sum_{s^\prime,r}p(s^\prime,r|s,a)[r+\gamma \sum_{a^\prime}\pi(a^\prime|s^\prime)q_\pi(s^\prime,a^\prime) \end{array} \\ \]

$$
\begin{array}{l}
q_\pi(s,a)  \overset{.}{=} E_\pi[G_t|S_t=s,A_t=a] \\
\qquad \quad \ = E_\pi[R_{t+1}+\gamma G_{t+1}|S_t=s,A_t=a] \\
\qquad \quad \ = \sum_{s^\prime,r}p(s^\prime,r|s,a)[r+\gamma \sum_{a^\prime}\pi(a^\prime|s^\prime)E_\pi[G_{t+1}|S_{t+1}=s^\prime,A_{t+1}=a^\prime]] \\
\qquad \quad \ = \sum_{s^\prime,r}p(s^\prime,r|s,a)[r+\gamma \sum_{a^\prime}\pi(a^\prime|s^\prime)q_\pi(s^\prime,a^\prime)
\end{array}
\\
$$