在两列文档中拆分方程式 - 拆分至第二列，而不是停留在第一列

Question 1

在您的 MWE 中没有定义\argmaxnor \givennor \cAnor \cS，所以无法编译，也错过了方程式中amssymb使用的命令的包。\mathbb{...}
包的使用aistats2021只与您的问题相关，因为它加载包，因此在 MWE 中，它可以被选项和包的加载amsmath所取代，就像下面的 MWE 中所做的那样twocolumn\documentclassamsmath
为了解决您的问题，您可以考虑使用 ˙multline math environment defined in theamsmath` 包。在其中，我尝试在您的方程式图像中重现 shoed 中的符号：

\documentclass[twocolumn,   % not needed when is loaded `aistats2021`
                twoside]{article}
%\usepackage{aistats2021}    % it is not relevant to your problem
\usepackage{amsmath,        % not needed when is loaded `aistats2021`
            amssymb}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\given}{?}    % it is not known, in equation is replaced by `\mid`
% \cA   % it is not known, in equation is replaced by `\mathcal{A}`
% \cS   % it is not known, in equation is replaced by `\mathcal{S}`

\usepackage{lipsum}         % text filler     

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{multline}\label{Eq:pi-mirror-descent}
\argmax_{\pi_h \in \Delta(\mathcal{A} \mid \mathcal{S})} 
    \mathbb{E}_{\pi^{k-1}} \Bigl[ 
        \left\langle Q_h^{k-1}(s_h \mid \cdot),\pi_h(\cdot\mid s_h)\right\rangle_{\mathcal{A}} \\
 +\frac{1}{\alpha}\mathcal{D}_{KL}\bigl(\pi_h(\cdot \mid s_h) \|\ \pi_h^{k-1}(\cdot \mid s_h)\bigr) 
                            \Bigr]
\end{multline}
\lipsum % text filler 
\end{document}

附录： 考虑到@daleif 的评论，上述 MWE 的序言和等式可以写成：

\documentclass[twocolumn, twoside]{article}
\usepackage{mathtools,       % needed, also when is loaded `aistats2021` which only provide `amsmath`
            amssymb}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclarePairedDelimiterX\given[2]()%        % <--- new
    {#1{}\delimsize\vert{}\mathopen{}#2}%   % <--- new
%\cA   % it is not known, in equation is replaced by `\mathcal{A}`
%\cS   % it is not known, in equation is replaced by `\mathcal{S}`

\usepackage{lipsum}         % text filler     

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{multline}\label{Eq:pi-mirror-descent}
\argmax_{\pi_h \in \Delta\given*{\mathcal{A}}{\mathcal{S}}} % <--- changed
    \mathbb{E}_{\pi^{k-1}} \Bigl[
        \left\langle Q_h^{k-1}  \given*{s_h}{\cdot},    % <--- changed
                     \pi_h      \given*{\cdot}{s_h}     % <--- changed
        \right\rangle_{\mathcal{A}} \\
% second line
 + \frac{1}{\alpha}\mathcal{D}_{KL}
    \left(\pi_h         \given*{s_h}{\cdot} % <--- changed
    \middle\|   % <--- new
          \pi_h^{k-1}   \given*{\cdot}{s_h} % <--- changed
    \right)
                            \Bigr]
    \end{multline}
\lipsum % text filler 
\end{document}

经过这些改变，方程现在如下所示：

Answer

在您的 MWE 中没有定义\argmaxnor \givennor \cAnor \cS，所以无法编译，也错过了方程式中amssymb使用的命令的包。\mathbb{...}
包的使用aistats2021只与您的问题相关，因为它加载包，因此在 MWE 中，它可以被选项和包的加载amsmath所取代，就像下面的 MWE 中所做的那样twocolumn\documentclassamsmath
为了解决您的问题，您可以考虑使用 ˙multline math environment defined in theamsmath` 包。在其中，我尝试在您的方程式图像中重现 shoed 中的符号：

\documentclass[twocolumn,   % not needed when is loaded `aistats2021`
                twoside]{article}
%\usepackage{aistats2021}    % it is not relevant to your problem
\usepackage{amsmath,        % not needed when is loaded `aistats2021`
            amssymb}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\given}{?}    % it is not known, in equation is replaced by `\mid`
% \cA   % it is not known, in equation is replaced by `\mathcal{A}`
% \cS   % it is not known, in equation is replaced by `\mathcal{S}`

\usepackage{lipsum}         % text filler     

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{multline}\label{Eq:pi-mirror-descent}
\argmax_{\pi_h \in \Delta(\mathcal{A} \mid \mathcal{S})} 
    \mathbb{E}_{\pi^{k-1}} \Bigl[ 
        \left\langle Q_h^{k-1}(s_h \mid \cdot),\pi_h(\cdot\mid s_h)\right\rangle_{\mathcal{A}} \\
 +\frac{1}{\alpha}\mathcal{D}_{KL}\bigl(\pi_h(\cdot \mid s_h) \|\ \pi_h^{k-1}(\cdot \mid s_h)\bigr) 
                            \Bigr]
\end{multline}
\lipsum % text filler 
\end{document}

附录： 考虑到@daleif 的评论，上述 MWE 的序言和等式可以写成：

\documentclass[twocolumn, twoside]{article}
\usepackage{mathtools,       % needed, also when is loaded `aistats2021` which only provide `amsmath`
            amssymb}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclarePairedDelimiterX\given[2]()%        % <--- new
    {#1{}\delimsize\vert{}\mathopen{}#2}%   % <--- new
%\cA   % it is not known, in equation is replaced by `\mathcal{A}`
%\cS   % it is not known, in equation is replaced by `\mathcal{S}`

\usepackage{lipsum}         % text filler     

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{multline}\label{Eq:pi-mirror-descent}
\argmax_{\pi_h \in \Delta\given*{\mathcal{A}}{\mathcal{S}}} % <--- changed
    \mathbb{E}_{\pi^{k-1}} \Bigl[
        \left\langle Q_h^{k-1}  \given*{s_h}{\cdot},    % <--- changed
                     \pi_h      \given*{\cdot}{s_h}     % <--- changed
        \right\rangle_{\mathcal{A}} \\
% second line
 + \frac{1}{\alpha}\mathcal{D}_{KL}
    \left(\pi_h         \given*{s_h}{\cdot} % <--- changed
    \middle\|   % <--- new
          \pi_h^{k-1}   \given*{\cdot}{s_h} % <--- changed
    \right)
                            \Bigr]
    \end{multline}
\lipsum % text filler 
\end{document}

经过这些改变，方程现在如下所示：

Question 2

您必须给出&您想要在split环境中对齐断点的位置的标志（如John Kormylo他在评论中提到的），另外由于错误，我刚刚\从您的代码中删除了它，请注意这一点......

一般情况下，断开操作符+ - X、符号等都要放在第二行缩进quad，修改后的MWE为：

\documentclass[twoside]{article}

\usepackage{aistats2021}
\usepackage{amsfonts}

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{equation}\label{Eq:pi-mirror-descent}
\begin{split}
&argmax_{\pi_h \in \Delta(cA \mid cS)} \mathbb{E}_{\pi^{k-1}} \Bigl [ \langle Q_h^{k-1}(s_h, \cdot),\pi_h(\cdot given s_h)\rangle_cA \\
&\quad +\frac{1}{\alpha}\mathcal{D}_{KL}\bigl(\pi_h(\cdot \mid s_h) \|\ \pi_h^{k-1}(\cdot \mid s_h)\bigr) \bigm]
\end{split}
\end{equation}
\end{document}

注意：我已添加amsfonts.sty以避免\mathbb错误...

Answer

您必须给出&您想要在split环境中对齐断点的位置的标志（如John Kormylo他在评论中提到的），另外由于错误，我刚刚\从您的代码中删除了它，请注意这一点......

一般情况下，断开操作符+ - X、符号等都要放在第二行缩进quad，修改后的MWE为：

\documentclass[twoside]{article}

\usepackage{aistats2021}
\usepackage{amsfonts}

\begin{document}
We recall the optimization problem here which is given below. Now consider why this broken this way.
\begin{equation}\label{Eq:pi-mirror-descent}
\begin{split}
&argmax_{\pi_h \in \Delta(cA \mid cS)} \mathbb{E}_{\pi^{k-1}} \Bigl [ \langle Q_h^{k-1}(s_h, \cdot),\pi_h(\cdot given s_h)\rangle_cA \\
&\quad +\frac{1}{\alpha}\mathcal{D}_{KL}\bigl(\pi_h(\cdot \mid s_h) \|\ \pi_h^{k-1}(\cdot \mid s_h)\bigr) \bigm]
\end{split}
\end{equation}
\end{document}

注意：我已添加amsfonts.sty以避免\mathbb错误...

在两列文档中拆分方程式 - 拆分至第二列，而不是停留在第一列

答案1

答案2

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