\documentclass[accepted]{uai2022} % for initial submission
% \documentclass[accepted]{uai2022} % after acceptance, for a revised
                                    % version; also before submission to
                                    % see how the non-anonymous paper
                                    % would look like
%% There is a class option to choose the math font
% \documentclass[mathfont=ptmx]{uai2022} % ptmx math instead of Computer
                                         % Modern (has noticable issues)
% \documentclass[mathfont=newtx]{uai2022} % newtx fonts (improves upon
                                          % ptmx; less tested, no support)
% NOTE: Only keep *one* line above as appropriate, as it will be replaced
%       automatically for papers to be published. Do not make any other
%       change above this note for an accepted version.

%% Choose your variant of English; be consistent

\usepackage[dvipsnames]{xcolor}
% \usepackage[colorlinks=true,linkcolor=darkblue,citecolor=darkblue,urlcolor=darkblue]{hyperref}

\usepackage[american]{babel}
% \usepackage[british]{babel}

%% Some suggested packages, as needed:
\usepackage{natbib} % has a nice set of citation styles and commands
    \bibliographystyle{plainnat}
    \renewcommand{\bibsection}{\subsubsection*{References}}
\usepackage{mathtools} % amsmath with fixes and additions
% \usepackage{siunitx} % for proper typesetting of numbers and units
\usepackage{booktabs} % commands to create good-looking tables
\usepackage{tikz} % nice language for creating drawings and diagrams

%% Provided macros
% \smaller: Because the class footnote size is essentially LaTeX's \small,
%           redefining \footnotesize, we provide the original \footnotesize
%           using this macro.
%           (Use only sparingly, e.g., in drawings, as it is quite small.)

%% Self-defined macros
\newcommand{\swap}[3][-]{#3#1#2} % just an example

\input{math_commands.tex}

\usepackage{url}

\usepackage{booktabs}       % professional-quality tables
\usepackage{amsfonts}       % blackboard math symbols
\usepackage{nicefrac}       % compact symbols for 1/2, etc.
\usepackage{microtype}      % microtypography

\usepackage{geometry}
\usepackage{amsmath}
\usepackage{amssymb}

\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{multirow}
\usepackage{makecell}
\usepackage{wrapfig}

\usepackage{caption}
%\usepackage{subcaption}
\usepackage{wrapfig}

\usepackage{algorithm,algpseudocode}
\usepackage{qiangstyle}
\usepackage{xr-hyper}


\makeatletter
\newcommand*{\addFileDependency}[1]{% argument=file name and extension
  \typeout{(#1)}
  \@addtofilelist{#1}
  \IfFileExists{#1}{}{\typeout{No file #1.}}
}
\makeatother

\newcommand*{\myexternaldocument}[1]{%
    \externaldocument{#1}%
    \addFileDependency{#1.tex}%
    \addFileDependency{#1.aux}%
}

\myexternaldocument{ye_162}

% \newcommand{\theHalgorithm}{\arabic{algorithm}}

% \title{Pareto Navigation Gradient Descent:
% a First-Order Algorithm for Optimization in Pareto Set}
\appendix
\onecolumn
\title{Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set}

% The standard author block has changed for UAI 2022 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
%
% Add authors
\author[1]{\href{mailto:<maoye21@utexas.edu>?Subject=Your UAI 2022 paper}{Mao Ye}{}}
\author[1]{Qiang Liu}
% Add affiliations after the authors
\affil[1]{%
    Computer Science Dept.\\
    The University of Texas at Austin.
}

  
\begin{document}

\global\long\def\th{\theta}%
\global\long\def\E{\mathrm{E}}%
\global\long\def\L{\vv{\ell}}%\text{L}}%
\global\long\def\dge{\succeq}%
\global\long\def\dle{\preceq}%
\global\long\def\dsqe{\succ}%
\global\long\def\dsle{\prec}%
\global\long\def\C{\mathcal{C}}%
\global\long\def\P{\mathcal{P}}%
\global\long\def\df{\mathrm{d}}
\global\long\def\tim{{t}}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{assumption}{Assumption}
\onecolumn
\maketitle

% \begin{acknowledgements} % will be removed in pdf for initial submission,
%                          % so you can already fill it to test with the
%                          % ‘accepted’ class option
%     Briefly acknowledge people and organizations here.

%     \emph{All} acknowledgements go in this section.
% \end{acknowledgements}





\input{tex/continous_proof} 
\clearpage
\input{tex/experiment_appendix}
\bibliography{uai2022-template}

\end{document}
