source/tex/command.tex

\usepackage[utf8]{inputenc} 
\usepackage[T1]{fontenc}    
\usepackage{lipsum,booktabs}
\usepackage{amsmath,mathrsfs,amssymb,amsfonts,bm}
\usepackage{rotating}
\usepackage{pdflscape}
\usepackage{tcolorbox}
\usepackage{hyperref,url,dsfont,nicefrac}
\usepackage{multirow}
\usepackage{makecell}
\usepackage{anyfontsize}
\usepackage{bbding}
\usepackage{paralist}
\usepackage{enumerate}
\hypersetup{
    colorlinks,
    breaklinks,
    linkcolor = blue,
    citecolor = blue,
    urlcolor  = black,
}
\allowdisplaybreaks
\usepackage{appendix}
\usepackage{multirow,makecell,tabularx}
\usepackage{xfrac}
\usepackage{nicefrac}
\usepackage{threeparttable}
\usepackage{pifont}
\usepackage{tikz}
\usepackage{wrapfig}
\usepackage{enumitem}
\usepackage{circledsteps}


\usepackage{algorithm}
\usepackage{algpseudocode}
\renewcommand{\algorithmicrequire}{ \textbf{Input:}}
\renewcommand{\algorithmicensure}{ \textbf{Output:}}
\newlength\myindent
\setlength\myindent{2em}
\newcommand\bindent{
  \begingroup
  \setlength{\itemindent}{\myindent}
  \addtolength{\algorithmicindent}{\myindent}
}
\newcommand\eindent{\endgroup}

\renewcommand{\tilde}{\widetilde}
\renewcommand{\hat}{\widehat}


\def \A {\mathcal{A}}
\def \Ah {\hat{A}}
\def \Bc {\mathcal{B}}

\def \B {\mathbb{B}}
\def \Bbf {\mathbf{B}}
\def \Bh {\hat{B}}


\def \C {\mathcal{C}}
\def \D {\mathcal{D}}
\def \E {\mathbb{E}}

\def \F {\mathcal{F}}
\def \Fb {\bar{F}}

\def \G {\mathcal{G}}
\def \H {\mathcal{H}}
\def \I {\mathcal{I}}
\def \J {\mathcal{J}}
\def \K {\mathcal{K}}
\def \L {\mathcal{L}}
\def \M {\mathcal{M}}
\def \N {\mathcal{N}}
\def \O {\mathcal{O}}
\def \Oh {\hat{\O}}
\def \Otil {\tilde{\O}}
\def \Q {\mathcal{Q}}

\def \R {\mathbb{R}}
\def \Rc {\mathcal{R}}
\def \Rbf {\mathbf{R}}

\def \cS {\mathcal{S}}
\def \Sbb {\mathbb{S}}

\def \T {\mathrm{T}}
\def \U {\mathcal{U}}
\def \V {\mathcal{V}}
\def \Vb {\bar{V}}
\def \Vh {\widehat{V}}

\def \W {\mathcal{W}}
\def \X {\mathcal{X}}
\def \Y {\mathcal{Y}}
\def \Z {\mathcal{Z}}

\def \a {\mathbf{a}}

\def \b {\mathbf{b}}

\def \c {\mathbf{c}}

\def \d {\mathbf{d}}
\def \db {\bar{d}}

\def \e {\boldsymbol{e}}
\def \eb {\mathbf{e}}

\def \f {\mathbf{f}}
\def \fh {\hat{f}}
\def \fb {\bar{f}}
\def \ft{\tilde{f}}

\def \g {\mathbf{g}}
\def \gh {\hat{\g}}
\def \gb {\bar{\g}}
\def \gt {\tilde{g}}
\def \tgb{\tilde{\mathbf{g}}}

\def \h {\mathbf{h}}

\def \htil {\tilde{h}}
\def \I {\mathbb{I}}
\def \j {\mathbf{j}}
\def \k {\mathbf{k}}

\def \Ltil {\tilde{L}} 
\def \l {\mathbf{l}}

\def \m {\boldsymbol{m}}
\def \mb {\mathbf{m}}
\def \mh {\hat{m}}

\def \n {\mathbf{n}}
\def \o {\mathbf{o}}
\def \p {\boldsymbol{p}}
\def \q {{\boldsymbol{q}}}

\def \r {\mathbf{r}}
\def \rb {\bar{r}}
\def \s {\mathbf{s}}
\def \t {\mathbf{t}}

\def \u {\mathbf{u}}

\def \v {\mathbf{v}}
\def \w {\mathbf{w}}
\def \x {\mathbf{x}}
\def \y {\mathbf{y}}
\def \z {\mathbf{z}}

\def \ph {\hat{p}}
\def \pb {\bar{p}}
\def \pt {\tilde{p}}
\def \pbh {\boldsymbol{\ph}}
\def \P {\mathbb{P}}
\def \qh {\hat{q}}
\def \qb {\bar{q}}
\def \qt {\tilde{q}}

\def \uh {\hat{\u}}
\def \ub {\bar{\u}}
\def \ut{\tilde{\u}}

\def \vh {\hat{\v}}
\def \vb {\bar{\v}}
\def \vt{\tilde{\v}}


\def \wh {\hat{\w}}
\def \wb {\boldsymbol{w}}
\def \wt {\tilde{\w}}
\def \ws {\w^\star}
\def \wbh {\hat{\boldsymbol{w}}}

\def \xh {\hat{\x}}
\def \xhh {\hat{x}}
\def \xb {\bar{\x}}
\def \xt {\tilde{\x}}
\def \xs {\x^\star}

\def \yh {\hat{\y}}
\def \yb {\bar{\y}}
\def \yt {\tilde{\y}}
\def \ys {\y^\star}

\def \zh {\hat{\z}}
\def \zb {\bar{\z}}
\def \zt {\tilde{\z}}

\def \mub {\boldsymbol{\mu}}

\def \epsilon {\varepsilon}
\def \Ecal {\mathcal{E}}
\def \Ot {\tilde{\O}}
\def \thetah {\hat{\theta}}

\def \sumI {\sum_{t \in \I}}
\def \sumT {\sum_{t=1}^T}
\def \sumt {\sum_{s=1}^t}
\def \sumTT {\sum_{t=2}^T}
\def \sumM {\sum_{j=1}^M}
\def \sumN {\sum_{i=1}^N}
\def \sumK {\sum_{k=1}^K}
\def \is {{i^\star}}
\def \js {{j^\star}}
\def \ks {{k^\star}}
\def \ith {{$i$\text{-th}}\xspace}

\def \KL {\textnormal{KL}}

\def \rightsym {\ding{51}}
\def \wrongsym {\ding{55}}

\def \ellb {\boldsymbol{\ell}}
\def \ellh {\hat{\ell}}
\def \ellbh {\hat{\ellb}}

\def \Reg {\textsc{Reg}}
\def \Dgap {\textsc{Dual-Gap}}
\def \AReg {\textsc{A-Reg}}
\def \SReg {\textnormal{S-Regret}}
\def \DReg {\textsc{D-Reg}}
\def \meta {\textsc{Meta-Reg}}
\def \base {\textsc{Base-Reg}}

\def \ader {\textsc{Ader}\xspace}
\def \OGD {\textsc{OGD}\xspace}
\def \OOMD {\textsc{OOMD}\xspace}
\def \mlprod {\textsc{Adapt-ML-Prod}\xspace}
\def \msmwc {\textsc{MsMwC}\xspace}
\def \msmwcM {\textsc{MsMwC-Top}\xspace}
\def \msmwcB {\textsc{MsMwC-Mid}\xspace}

\def \exp {\text{exp}}
\def \sc {\text{sc}}
\def \les {\lesssim}

\newcommand{\rom}[1]{\setcounter{romancounter}{#1}\textit{(\roman{romancounter})}}


\usepackage{mathtools}
\usepackage{autobreak}
\let\oldnorm\norm  
\let\norm\undefined 

\newcommand\norm[1]{\left\| #1 \right\|}
\newcommand\normop[1]{\left\| #1 \right\|_{\textnormal{op}}}
\newcommand\normF[1]{\left\| #1 \right\|_{\textnormal{F}}}
\newcommand\abs[1]{\left| #1 \right|}

\newcommand\inner[2]{\langle #1, #2 \rangle}
\newcommand\ceil[1]{\lceil #1 \rceil}
\newcommand*\diff{\mathop{}\!\mathrm{d}}
\newcommand*\Diff[1]{\mathop{}\!\mathrm{d^#1}}
\newcommand\ind[1]{\mathds{1}_{\{#1\}}}
\newcommand\sbr[1]{\left( #1 \right)}
\newcommand\mbr[1]{\left[ #1 \right]}
\newcommand\bbr[1]{\left\{ #1 \right\}}
\newcommand\bigbr[1]{\big(#1 \big)}\newcommand\biggbr[1]{\bigg(#1 \bigg)}
\newcommand\term[1]{\text{\textsc{term}~(\textsc{#1})}}
\newcommand\given[1][]{\:#1\vert\:}
\newcommand\givenn[1][]{\:#1\middle\vert\:}
\newcommand\seq[1]{\{#1\}_{t=1}^T}

\DeclareMathOperator{\proj}{Proj}
\DeclareMathOperator{\indicator}{\mathds{1}}

\DeclareMathOperator*{\poly}{poly}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator{\Tr}{Tr}
\def \define {\triangleq}
\def \one {\mathbf{1}}
\def \zero {\mathbf{0}}

\numberwithin{equation}{section}


\def \ohedge {\textsf{Optimistic-Hedge}\xspace}


\let\proof\relax
\let\endproof\relax
\usepackage{amsthm}
\let\proof\relax
\let\endproof\relax
\def \endenv {\hfill\raisebox{1pt}{$\P$}\smallskip}
\newenvironment{proof}{\par\noindent{\bf Proof\ }}{\hfill\qedsymbol\\[2mm]}
\renewcommand\qedsymbol{$\blacksquare$}



\newtheorem{Theorem}{Theorem}
\newtheorem{Lemma}{Lemma}
\newtheorem{Corollary}{Corollary}

\theoremstyle{definition}
\newtheorem{Fact}{Fact}
\newtheorem{Claim}{Claim}
\newtheorem{Observation}{Observation}
\newtheorem{Proposition}{Proposition}
\newtheorem{Property}{Property}
\newtheorem{Definition}{Definition}
\newtheorem{Condition}{Condition}
\newtheorem{Assumption}{Assumption}
\newtheorem{Conjecture}{Conjecture}
\newtheorem{Example}{Example}
\definecolor{darkgreen}{RGB}{0,100,0}
\newtheorem{NoteTemp}{Note}
\newenvironment{Note}{\color{darkgreen}\begin{NoteTemp}}{\end{NoteTemp}}
\newtheorem{Problem}{Problem}
\newtheorem{Remark}{Remark}
\newtheorem*{ProofSketch}{Proof Sketch}
\newtheorem*{Analysis}{\underline{Analysis}} 


\usepackage{graphicx,subfigure} 

\newcommand\itbf[1]{\textit{\textbf{#1}}}
\definecolor{myred}{RGB}{192,0,1}
\newcommand\red[1]{{\color{myred} #1}}
\newcommand\ritbf[1]{{\color{myred} \textit{\textbf{#1}}}}
\definecolor{myblue}{RGB}{68,114,196}
\newcommand\blue[1]{{\color{myblue} #1}}
\newcommand\bitbf[1]{{\color{myblue} \textit{\textbf{#1}}}}
\definecolor{mygreen}{RGB}{0,128,0}
\newcommand\green[1]{{\color{mygreen} #1}}
\newcommand\gitbf[1]{{\color{mygreen} \textit{\textbf{#1}}}}


\definecolor{myorange}{RGB}{230,120,0}
\newcommand\orange[1]{{\color{myorange} #1}}
\newcommand\oitbf[1]{{\color{myorange} \textit{\textbf{#1}}}}


\definecolor{mypurple}{RGB}{110,0,160}
\newcommand\purple[1]{{\color{mypurple} #1}}
\newcommand\pitbf[1]{{\color{mypurple} \textit{\textbf{#1}}}}
\newcommand{\Authornote}[2]{{\small\textcolor{myblue}{\sf$<<<${  #1: #2}$>>>$}}}
\newcommand{\Authormarginnote}[2]{\marginpar{\parbox{2cm}{\raggedright\tiny \textcolor{DSgray}{#1: #2}}}}
\newcommand{\yhnote}[1]{{\Authornote{Hang}{#1}}}
\newcommand{\yyhnote}[1]{{\small\textcolor{myred}{\sf$<<<${  Yu-Hu: #1}$>>>$}}}

\providecommand{\keywords}[1]
{
  \small	
  \textbf{\textit{Keywords---}} #1
}


\usepackage{prettyref}
\newcommand{\pref}[1]{\prettyref{#1}}
\newcommand{\pfref}[1]{Proof of \prettyref{#1}}
\newcommand{\savehyperref}[2]{\texorpdfstring{\hyperref[#1]{#2}}{#2}}
\newrefformat{eq}{\savehyperref{#1}{Eq.~\textup{(\ref*{#1})}}}
\newrefformat{eqn}{\savehyperref{#1}{Eq.~(\ref*{#1})}}
\newrefformat{lem}{\savehyperref{#1}{Lemma~\ref*{#1}}}
\newrefformat{lemma}{\savehyperref{#1}{Lemma~\ref*{#1}}}
\newrefformat{def}{\savehyperref{#1}{Definition~\ref*{#1}}}
\newrefformat{line}{\savehyperref{#1}{Line~\ref*{#1}}}
\newrefformat{thm}{\savehyperref{#1}{Theorem~\ref*{#1}}}
\newrefformat{cond}{\savehyperref{#1}{Condition~\ref*{#1}}}
\newrefformat{table}{\savehyperref{#1}{Table~\ref*{#1}}}
\newrefformat{corr}{\savehyperref{#1}{Corollary~\ref*{#1}}}
\newrefformat{cor}{\savehyperref{#1}{Corollary~\ref*{#1}}}
\newrefformat{sec}{\savehyperref{#1}{Section~\ref*{#1}}}
\newrefformat{subsec}{\savehyperref{#1}{Section~\ref*{#1}}}
\newrefformat{app}{\savehyperref{#1}{Appendix~\ref*{#1}}}
\newrefformat{appendix}{\savehyperref{#1}{Appendix~\ref*{#1}}}
\newrefformat{ass}{\savehyperref{#1}{Assumption~\ref*{#1}}}
\newrefformat{assum}{\savehyperref{#1}{Assumption~\ref*{#1}}}
\newrefformat{ex}{\savehyperref{#1}{Example~\ref*{#1}}}
\newrefformat{fig}{\savehyperref{#1}{Figure~\ref*{#1}}}
\newrefformat{alg}{\savehyperref{#1}{Algorithm~\ref*{#1}}}
\newrefformat{remark}{\savehyperref{#1}{Remark~\ref*{#1}}}
\newrefformat{conj}{\savehyperref{#1}{Conjecture~\ref*{#1}}}
\newrefformat{prop}{\savehyperref{#1}{Proposition~\ref*{#1}}}
\newrefformat{proto}{\savehyperref{#1}{Protocol~\ref*{#1}}}
\newrefformat{prob}{\savehyperref{#1}{Problem~\ref*{#1}}}
\newrefformat{claim}{\savehyperref{#1}{Claim~\ref*{#1}}}
\newrefformat{que}{\savehyperref{#1}{Question~\ref*{#1}}}
\newrefformat{op}{\savehyperref{#1}{Open Problem~\ref*{#1}}}
\newrefformat{fn}{\savehyperref{#1}{Footnote~\ref*{#1}}}
\newrefformat{require}{\savehyperref{#1}{Requirement~\ref*{#1}}}
\newcommand{\qedbox}{\par\hfill $\blacksquare$}

\def \mix {\textnormal{\textsc{mix}}}