常用LaTex語法

符號

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

等號/箭頭	\(\approx\)	\(\sim\)	\(\propto\)	\(\geq\)	\(\leq\)	\(\Rightarrow\)	\(\Longrightarrow\)	\(\rightrightarrows\)	\(\rightleftarrows\)
LaTex	\approx	\sim	\propto	\geq	\leq	\Rightarrow	\Longrightarrow	\rightrightarrows	\rightleftarrows

運算子	\(\prod\)	\(\sum\)	\(\int\)	\(\partial x\)	\(\nabla\)	\(\in\)	\(\not\in\)	\(\subset\)	\(\not\subset\)	\(a \cdot b\)	\(a \times b\)	\(a \div b\)
LaTex	\prod	\sum	\int	\partial x	\nabla	\in	\not\in	\subset	\not\subset	a \cdot b	a \times b	a \div b

上/下劃線	\(\widetilde x\)	\(\overline{\text{x}}\)	\(\widetilde x\)	\(\tilde x\)	\(\underline{V}_{n}\)	\(\overline V_n\)
LaTex	\widetilde x	\overline{\text{x}}	\widetilde x	\tilde x	\underline{V}_{n}	\overline{V}_n

絕對值/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{T}	\mathcal{T}	\mathscr{T}	\mathsf{T}	\mathtt{T}	\mathit{T}

公式

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

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

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

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

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

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

常用LaTex語法