我正在使用sty文件和包编写算法的伪代码。我的问题是如何才能将其放在一行中？aistats2021.styalgorithmicalgorithmline 14
这是乳胶代码。
\documentclass[twoside]{article}
\usepackage{aistats2021}
\usepackage{algorithmic}
\usepackage{algorithm}
\begin{document}
\begin{algorithm}[t]
\caption{\label{Algorithm-TS} Algo }
\begin{algorithmic}[1]
\STATE Initialize $\{Q^0_h\}_{h=1}^H$ as zero functions and $\{\pi^0_h\}_{h=1}^H$ as uniform distributions on $\cA$. \label{line:winit}
\STATE \textbf{For} episode $k=1,2,\ldots, K$ \textbf{do}
\STATE \hspace{0.15in} Receive the initial state $s_1^k$.
\STATE \hspace{0.15in} \textbf{For} step {$h=1, 2, \ldots, H$} \textbf{do} \label{line:pis-start}
\STATE \hspace{0.30in} Update policy
\STATE \hspace{0.45in} $\pi^k_h (\cdot \,|\, \cdot) \propto \pi^{k-1}_h(\cdot \,|\, \cdot) \cdot \exp\{\alpha Q^{k-1}_h(\cdot , \cdot)\}$ \label{line:policy-improvement}
\STATE \hspace{0.30in} Take the action following $a^k_h\sim\pi^k_h(\cdot\,|\,s_h^k)$.
\STATE \hspace{0.30in} Observe reward $r_h(s_h^k,a^k_h)$ and
\STATE \hspace{0.45in} get next state $s^k_{t+1}$. \label{line:pis-end}
\STATE \hspace{0.15in} Initialize $V^k_{H+1}$ as a zero function.
\STATE \hspace{0.15in} \textbf{For} step {$h=H, H-1,\ldots, 1$} \textbf{do}\label{line:pes-start}
\STATE \hspace{0.30in} $\hat{w}^k_h \leftarrow (\Lambda^{k}_h)^{-1} \sum_{i=1}^{k-1} r_h(s_h^i, a_h^i) \varphi(s_h^i,a_h^i) $. \label{line:w-hat}
\STATE \hspace{0.30in} Sample i.i.d. $\{\epsilon^{k,j}_h\}_{j \in [M]} \sim \mathcal{N}(0,\sigma^2_2(\Lambda^{k}_h)^{-1}) $.\label{line:r_noise-sample}\
\STATE \hspace{0.30in} $\Tilde{P}_h\Tilde{V}^{k,j}_{h+1}(\cdot,\cdot) \leftarrow \phi_h^{k}(\cdot, \cdot)^\top(\hat{\theta}^k_h + \xi^{k,j}_h)$ for $j \in [M]$.
\label{line:PVh_plus_1_tilde_perturbed}
\STATE \hspace{0.30in} $\Tilde{r}^{k,j}_h(\cdot,\cdot) \leftarrow \varphi(\cdot, \cdot)^\top(\hat{w}^k_h + \epsilon^{k,j}_h)$ for $j \in [M]$.\label{line:r_tilde_perturbed}
\STATE \hspace{0.30in} $V^k_h(\cdot) \leftarrow \langle Q^k_h(\cdot,\cdot), \pi^k_h(\cdot\,|\,\cdot) \rangle_{\cA}$.\label{line:pes-end}
\end{algorithmic}
% \end{spacing}
\end{algorithm}
\end{document}
以下是aistats2021.sty重现此过程的。
% File: aistats2021.sty
% Modified by Robert Giaquinto and Krikamol Muandet 2021: changed
% venue, year, and volume number. Adjust spacing in the copyright box.
%
% Modified by Marcello Restelli, 2020: changed \evensidemargin and
% \oddsidemargin in order to center the text with respect to the page.
% Removed author names and affiliation when the paper is submitted.
% Added command to display acknowledgments only in the final version.
%
% Modified by Roberto Calandra, 2019: introduced parametric structure to
% change venue, year, and volume number. This will make life easier
% for future organizers :)
%
% Modified Atsushi Miyauchi, Mirai Tanaka and Akiko Takeda, 2018: changed venue,
% year, volume number, and heading for the references, and removed tiny bugs.
%
% Modified Fernando Perez-Cruz, 2017: changed venue, year, and volume number.
%
% Modified Scott Alfeld, 2016: changed venue, year, and volume number.
%
% Modified Zoltan Szabo, 2015: change venue, year, volume number.
%
% Modified Antti Honkela, 2013: change venue, year
%
% Modified Miro Dudik, 2011, 2012: change venue, year and volume number
%
% Modified Geoff Gordon, 2010: change to 2011
%
% Modified Mauricio Alvarez, 2009. Headings for the manuscript when
% being under review and additional changes so that the headings are
% automatically obtained from the title and author fields from the tex
% file. Also changes to the year 2009 for 2010 where it appeared.
%
% Modified Mauricio Alvarez, 2009. Copyright Notice and commands for headings
%
%
% Originally this file contains the LaTeX formatting parameters for the Morgan
% Kaufmann two column, 8 1/2 by 11 inch proceedings format.
\NeedsTeXFormat{LaTeX2e}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Content to be changed from year to year
\ProvidesPackage{aistats2021}[2020/08/23 AISTATS2021 submission/camera-ready style file]
\newcommand{\@conferenceordinal}{24\textsuperscript{th}}
\newcommand{\@conferenceyear}{2021}
\newcommand{\@conferencelocation}{San Diego, California, USA}
\newcommand{\@conferencevolume}{130} % To be assigned by JMLR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{amsmath}
% Create acknowledgments -- only if the option 'final' is activated
\providecommand{\acknowledgments}[1]{}
\newcommand{\ackaccepted}[1]{%
\subsubsection*{Acknowledgments} #1
}
\DeclareOption{accepted}{\renewcommand{\statePaper}{\acceptedPaper}%
\renewcommand{\Notice@String}{\AISTATS@appearing}%
\renewcommand{\acknowledgments}{\ackaccepted}}
\newcommand{\statePaper}{0}
\newcommand{\acceptedPaper}{1}
\newcommand{\Notice@String}{Preliminary work. Under review by AISTATS \@conferenceyear. Do not distribute.}
\newcommand{\AISTATS@appearing}{Proceedings of the \@conferenceordinal\,International Conference on Artificial
Intelligence and Statistics (AISTATS) \@conferenceyear, \@conferencelocation\@. PMLR: Volume \@conferencevolume. Copyright
\@conferenceyear\/ by the author(s).}
\ProcessOptions\relax
\evensidemargin -0.125in
\oddsidemargin -0.125in
\setlength\topmargin{-25pt} \setlength\textheight{9.25in}
\setlength\textwidth{6.75in} \setlength\columnsep{0.25in}
\newlength\titlebox \setlength\titlebox{2.375in}
\setlength\headheight{10pt} \setlength\headsep{15pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% To include the copyright legend at the end of
%%%% the first column of the first page. Adapted from ICML09.sty
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\ftype@copyrightbox{8}
\def\@copyrightspace{
% Create a float object positioned at the bottom of the column. Note
% that because of the mystical nature of floats, this has to be called
% before the first column is populated with text (e.g., from the title
% or abstract blocks). Otherwise, the text will force the float to
% the next column. -- TDRL.
\@float{copyrightbox}[b]
\begin{center}
\setlength{\unitlength}{1pc}
\begin{picture}(20,2.5)
% Create a line separating the main text from the note block.
% 4.818pc==0.8in.
\put(0,3.5){\line(1,0){4.818}}
% Insert the text string itself. Note that the string has to be
% enclosed in a parbox -- the \put call needs a box object to
% position. Without the parbox, the text gets splattered across the
% bottom of the page semi-randomly. The 19.75pc distance seems to be
% the width of the column, though I can't find an appropriate distance
% variable to substitute here. -- TDRL.
\put(0,0){\parbox[b]{19.75pc}{\small \Notice@String}}
\end{picture}
\end{center}
\end@float}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength\footskip{0pt}
\thispagestyle{empty} \pagestyle{empty}
\flushbottom \twocolumn \sloppy
\def\addcontentsline#1#2#3{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Definition of maketitle (includes title and author)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{fancyhdr}
% box to check the size of the running head
\newbox\titrun
\newbox\autrun
% general page style
\pagestyle{fancy}
\renewcommand{\headrulewidth}{0pt}
\fancyhead{}
\fancyfoot{}
% definition to set running head title and running head author
\def\runningtitle#1{\gdef\@runningtitle{#1}}
\def\runningauthor#1{\gdef\@runningauthor{#1}}
\long\def\aistatstitle#1{
%\renewcommand{\headrulewidth}{0.5pt}
\gdef\@runningheadingerrortitle{0}
% If paper is under review print this as headings
\ifnum\statePaper=0
{
\gdef\@runningtitle{Manuscript under review by AISTATS \@conferenceyear}
}
\fi
% If the paper is accepted, print the title or the running title as heading.
\ifnum\statePaper=1
{
\ifx\undefined\@runningtitle
{
\gdef\@runningtitle{#1}
}
\fi
}
\fi
\ifnum\@runningheadingerrortitle=0
{
\global\setbox\titrun=\vbox{\small\bfseries\@runningtitle}%
\ifdim\wd\titrun>\textwidth%
{\gdef\@runningheadingerrortitle{2}
\gdef\@messagetitle{Running heading title too long}
}%
\else\ifdim\ht\titrun>10pt
{\gdef\@runningheadingerrortitle{3}
\gdef\@messagetitle{Running heading title breaks the line}
}%
\fi
\fi
}
\fi
\ifnum\@runningheadingerrortitle>0
{
\fancyhead[CE]{\small\bfseries\@messagetitle}
\ifnum\@runningheadingerrortitle>1
\typeout{}%
\typeout{}%
\typeout{*******************************************************}%
\typeout{Running heading title exceeds size limitations for running head.}%
\typeout{Please supply a shorter form for the running head}
\typeout{with \string\runningtitle{...}\space just after \string\begin{document}}%
\typeout{*******************************************************}%
\typeout{}%
\typeout{}%
\fi
}
\else
{
\fancyhead[CE]{\small\bfseries\@runningtitle}
}
\fi
\hsize\textwidth
\linewidth\hsize \toptitlebar {\centering
{\Large\bfseries #1 \par}}
\bottomtitlebar \vskip 0.2in plus 1fil minus 0.1in
}
\long\def\aistatsauthor#1{
\gdef\@runningheadingerrorauthor{0}
% If the paper is under review, print this message as heading.
\ifnum\statePaper=0
{
\gdef\@runningauthor{Manuscript under review by AISTATS \@conferenceyear}
}
\fi
% If the paper is accepted, print the author names or runningauthor as heading.
\ifnum\statePaper=1
{
\ifx\undefined\@runningauthor%
{
\gdef\@runningauthor{\def\and{\unskip{,}\enspace}\def\And{\unskip{,}\enspace}\def\AND{\unskip{,}\enspace}
#1}
}
\fi
}
\fi
\ifnum\@runningheadingerrorauthor=0
{
\global\setbox\autrun=\vbox{\small\bfseries\@runningauthor}
\ifdim\wd\autrun>\textwidth%
{\gdef\@runningheadingerrorauthor{2}
\gdef\@messageauthor{Running heading author too long}
}%
\else\ifdim\ht\autrun>10pt
{\gdef\@runningheadingerrorauthor{3}
\gdef\@messageauthor{Running heading author breaks the line}
}%
\fi
\fi
}
\fi
\ifnum\@runningheadingerrorauthor>0
{
\fancyhead[CO]{\small\bfseries\@messageauthor}
\ifnum\@runningheadingerrorauthor>1
\typeout{}%
\typeout{}%
\typeout{*******************************************************}%
\typeout{Running heading author exceeds size limitations for running head.}%
\typeout{Please supply a shorter form for the running head}
\typeout{with \string\runningauthor{...}\space just after \string\begin{document}}%
\typeout{*******************************************************}%
\typeout{}%
\typeout{}%
\fi
}
\else
{
\fancyhead[CO]{\small\bfseries\@runningauthor}
}
\fi
\ifnum\statePaper=0
{
{\def\and{\unskip\enspace{\rm and}\enspace}%
\def\And{\end{tabular}\hss \egroup \hskip 1in plus 2fil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}%
\def\AND{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}
\def\ANDD{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries Anonymous Author
\end{tabular}
\hss\egroup
\hfil\hfil\egroup}
}
\else
{
{\def\and{\unskip\enspace{\rm and}\enspace}%
\def\And{\end{tabular}\hss \egroup \hskip 1in plus 2fil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}%
\def\AND{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}
\def\ANDD{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries}
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\bfseries #1
\end{tabular}
\hss\egroup
\hfil\hfil\egroup}
}
\fi
}
\long\def\aistatsaddress#1{
\ifnum\statePaper=0
{
{\def\and{\unskip\enspace{\rm and}\enspace}%
\def\And{\end{tabular}\hss \egroup \hskip 1in plus 2fil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c} }%
\def\AND{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt \bgroup \hss \begin{tabular}[t]{c}}
\def\ANDD{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth \bgroup \hfil\hfil
\hbox to 0pt \bgroup \hss\begin{tabular}[t]{c}\bfseries}
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}
Anonymous Institution
\end{tabular}
\hss\egroup
\hfil\hfil\egroup}
\vskip 0.3in plus 2fil minus 0.1in
}
\else
{
{\def\and{\unskip\enspace{\rm and}\enspace}%
\def\And{\end{tabular}\hss \egroup \hskip 1in plus 2fil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c} }%
\def\AND{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt \bgroup \hss \begin{tabular}[t]{c}}
\def\ANDD{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.25in plus 1fil minus 0.125in
\hbox to \linewidth \bgroup \hfil\hfil
\hbox to 0pt \bgroup \hss\begin{tabular}[t]{c}\bfseries}
\hbox to \linewidth\bgroup \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c} #1
\end{tabular}
\hss\egroup
\hfil\hfil\egroup}
\vskip 0.3in plus 2fil minus 0.1in
}
\fi
}
\renewcommand{\headrulewidth}{0.5pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Definition of abstract environment
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewenvironment{abstract}
{\@copyrightspace\centerline{\large\bfseries
Abstract}\vspace{0.5ex}\begin{quote}}{\par\end{quote}\vskip 1ex}
% sections with less space
\def\section{\@startsection {section}{1}{\z@}{-2.0ex plus
-0.5ex minus -.2ex}{1.5ex plus 0.3ex minus .2ex}{\large\bfseries\raggedright}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-1.8ex plus
-0.5ex minus -.2ex}{0.8ex plus .2ex}{\normalsize\bfseries\raggedright}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-1.5ex plus
-0.5ex minus -.2ex}{0.5ex plus .2ex}{\normalsize\bfseries\raggedright}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{1.5ex plus
0.5ex minus .2ex}{-1em}{\normalsize\bfseries}}
\def\subparagraph{\@startsection{subparagraph}{5}{\z@}{1.5ex plus
0.5ex minus .2ex}{-1em}{\normalsize\bfseries}}
\def\subsubsubsection{\vskip 5pt{\noindent\normalsize\rm\raggedright}}
% Footnotes
\footnotesep 6.65pt %
\skip\footins 9pt plus 4pt minus 2pt
\def\footnoterule{\kern-3pt \hrule width 5pc \kern 2.6pt }
\setcounter{footnote}{0}
% Lists and paragraphs
\parindent 0pt
\topsep 4pt plus 1pt minus 2pt
\partopsep 1pt plus 0.5pt minus 0.5pt
\itemsep 2pt plus 1pt minus 0.5pt
\parsep 2pt plus 1pt minus 0.5pt
\parskip .5pc
\leftmargin 2em \leftmargini\leftmargin \leftmarginii 2em
\leftmarginiii 1.5em \leftmarginiv 1.0em \leftmarginv .5em
\leftmarginvi .5em
\labelwidth\leftmargini\advance\labelwidth-\labelsep \labelsep 5pt
\def\@listi{\leftmargin\leftmargini}
\def\@listii{\leftmargin\leftmarginii
\labelwidth\leftmarginii\advance\labelwidth-\labelsep
\topsep 2pt plus 1pt minus 0.5pt
\parsep 1pt plus 0.5pt minus 0.5pt
\itemsep \parsep}
\def\@listiii{\leftmargin\leftmarginiii
\labelwidth\leftmarginiii\advance\labelwidth-\labelsep
\topsep 1pt plus 0.5pt minus 0.5pt
\parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt
\itemsep \topsep}
\def\@listiv{\leftmargin\leftmarginiv
\labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
\labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
\labelwidth\leftmarginvi\advance\labelwidth-\labelsep}
\abovedisplayskip 7pt plus2pt minus5pt%
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip 0pt plus3pt%
\belowdisplayshortskip 4pt plus3pt minus3pt%
% Less leading in most fonts (due to the narrow columns)
% The choices were between 1-pt and 1.5-pt leading
\def\@normalsize{\@setsize\normalsize{11pt}\xpt\@xpt}
\def\small{\@setsize\small{10pt}\ixpt\@ixpt}
\def\footnotesize{\@setsize\footnotesize{10pt}\ixpt\@ixpt}
\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{20pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{23pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{28pt}\xxvpt\@xxvpt}
\def\toptitlebar{
\hrule height4pt
\vskip .25in}
\def\bottomtitlebar{
\vskip .25in
\hrule height1pt
\vskip .25in}
\renewenvironment{thebibliography}[1]
{\subsubsection*{\refname}%
\@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}%
\list{\@biblabel{\@arabic\c@enumiv}}%
{\settowidth\labelwidth{\@biblabel{#1}}%
\leftmargin\labelwidth
\advance\leftmargin\labelsep
\@openbib@code
\usecounter{enumiv}%
\let\p@enumiv\@empty
\renewcommand\theenumiv{\@arabic\c@enumiv}}%
\sloppy
\clubpenalty4000
\@clubpenalty \clubpenalty
\widowpenalty4000%
\sfcode`\.\@m}
{\def\@noitemerr
{\@latex@warning{Empty `thebibliography' environment}}%
\endlist}
答案1
我将所有出现的 替换\hspace{0.30in}为qquad，并将转置符号更靠近右括号（添加 -5mu 的数学字距调整）。无关：我认为\widetilde大写字母看起来更好。
\documentclass[twoside]{article}
\usepackage{aistats2021}
\usepackage{algorithmic}
\usepackage{algorithm}
\newcommand*{\cA}{\mathcal{A}}
\begin{document}
\begin{algorithm}[t]
\caption{\label{Algorithm-TS} Algo }
\begin{algorithmic}[1]
\STATE Initialize $\{Q^0_h\}_{h=1}^H$ as zero functions and $\{\pi^0_h\}_{h=1}^H$ as uniform distributions on $\cA$. \label{line:winit}
\STATE \textbf{For} episode $k=1,2,\ldots, K$ \textbf{do}
\STATE \hspace{0.15in} Receive the initial state $s_1^k$.
\STATE \hspace{0.15in} \textbf{For} step {$h=1, 2, \ldots, H$} \textbf{do} \label{line:pis-start}
\STATE \qquad Update policy
\STATE \hspace{0.45in} $\pi^k_h (\cdot \,|\, \cdot) \propto \pi^{k-1}_h(\cdot \,|\, \cdot) \cdot \exp\{\alpha Q^{k-1}_h(\cdot , \cdot)\}$ \label{line:policy-improvement}
\STATE \qquad Take the action following $a^k_h\sim\pi^k_h(\cdot\,|\,s_h^k)$.
\STATE \qquad Observe reward $r_h(s_h^k,a^k_h)$ and
\STATE \hspace{0.45in} get next state $s^k_{t+1}$. \label{line:pis-end}
\STATE \hspace{0.15in} Initialize $V^k_{H+1}$ as a zero function.
\STATE \hspace{0.15in} \textbf{For} step {$h=H, H-1,\ldots, 1$} \textbf{do}\label{line:pes-start}
\STATE \qquad $\hat{w}^k_h \leftarrow (\Lambda^{k}_h)^{-1} \sum_{i=1}^{k-1} r_h(s_h^i, a_h^i) \varphi(s_h^i,a_h^i) $. \label{line:w-hat}
\STATE \qquad Sample i.i.d. $\{\epsilon^{k,j}_h\}_{j \in [M]} \sim \mathcal{N}(0,\sigma^2_2(\Lambda^{k}_h)^{-1}) $.\label{line:r_noise-sample}\
\STATE \qquad $\widetilde{P}_h\widetilde{V}^{k,j}_{h+1}(\cdot,\cdot) \leftarrow \phi_h^{k}(\cdot, \cdot)^{\mkern-4mu\top}(\hat{\theta}^k_h + \xi^{k,j}_h)$ \rlap{for $j \in [M]$.}
\label{line:PVh_plus_1_tilde_perturbed}
\STATE \qquad
$\Tilde{r}^{k,j}_h(\cdot,\cdot) \leftarrow \varphi(\cdot, \cdot)^{\mkern-4mu\top}(\hat{w}^k_h + \epsilon^{k,j}_h)$ for $j \in [M]$.\label{line:r_tilde_perturbed}
\STATE \qquad $V^k_h(\cdot) \leftarrow \langle Q^k_h(\cdot,\cdot), \pi^k_h(\cdot\,|\,\cdot) \rangle_{\cA}$.\label{line:pes-end}
\end{algorithmic}
% \end{spacing}
\end{algorithm}
\end{document}
