% Useful text commands
\newcommand{\hr}{\begin{center}\rule{0.5\linewidth}{\linethickness}\end{center}}

% Abbreviations
\newcommand{\ie}{\emph{i.e.}}
\newcommand{\iid}{\emph{i.i.d.}}
\newcommand{\eg}{\emph{e.g.}}
\newcommand{\cf}{\emph{cf}}

\newcommand{\hook}{\newline\ensuremath{\hookrightarrow}\;}
\newcommand{\citationright}[1]{\hfill{}\tiny{\textcolor{gray}{#1}}\normalsize}
\newcommand{\citationbottomright}[1]{\vfill{}\hfill{}\tiny{\textcolor{gray}{#1}}\normalsize}
\newcommand{\citationbottomrightsmall}[1]{\vfill{}\hfill{}\small{\textcolor{gray}{#1}}\normalsize}

% Maths
\newcommand{\bigO}[1]{\ensuremath{\mathop{}\mathopen{}\mathcal{O}\mathopen{}\left(#1\right)}}
\newcommand{\smallO}[1]{\ensuremath{\mathop{}\mathopen{}o\mathopen{}\left(#1\right)}}

\newcommand{\E}{\mathbb{E}}
\renewcommand{\Pr}{\mathbb{P}}
\newcommand{\indic}{\mathbbm{1}}

\newcommand{\kl}{\ensuremath{\mathrm{kl}}}
\newcommand{\KL}{\ensuremath{\mathrm{KL}}}
\newcommand{\Ccal}{\mathcal{C}}

% Algorithms
\newcommand{\UCBalpha}{\ensuremath{\mathrm{UCB}_{\alpha}}}
\newcommand{\UCB}{\ensuremath{\mathrm{UCB}_1}}
\newcommand{\UCBH}{\ensuremath{\mathrm{UCB}}-\ensuremath{\mathrm{H}}}
\newcommand{\ExpThree}{\ensuremath{\mathrm{Exp}3}}
\newcommand{\BayesUCB}{\ensuremath{\mathrm{Bayes}\mathrm{UCB}}}
\newcommand{\klUCB}{\ensuremath{\mathrm{kl}\text{-}\mathrm{UCB}}}
\newcommand{\KLUCB}{\ensuremath{\mathrm{KL}\text{-}\mathrm{UCB}}}
\newcommand{\rhoRand}{\ensuremath{\mathrm{Rho}\mathrm{Rand}}}
\newcommand{\RhoRand}{\ensuremath{\mathrm{Rho}\mathrm{Rand}}}
\newcommand{\rhoFixedRank}{\ensuremath{\mathrm{Rho}\mathrm{FixedRank}}}
\newcommand{\rhoRandRot}{\ensuremath{\mathrm{Rho}\mathrm{Rand}\mathrm{Rot}}}
\newcommand{\rhoRandSticky}{\ensuremath{\mathrm{Rho}\mathrm{Rand}\mathrm{Sticky}}}
\newcommand{\rhoRandALOHA}{\ensuremath{\mathrm{Rho}\mathrm{Rand}\mathrm{ALOHA}}}
\newcommand{\rhoLearn}{\ensuremath{\mathrm{Rho}\mathrm{Learn}}}
\newcommand{\rhoRandEst}{\ensuremath{\mathrm{Rho}\mathrm{Est}}}
%
\newcommand{\rhoRandUCB}{\ensuremath{\mathrm{Rho}\mathrm{Rand}\text{-}\mathrm{UCB}_1}}
\newcommand{\rhoRandklUCB}{\ensuremath{\mathrm{Rho}\mathrm{Rand}\text{-}\mathrm{KLUCB}}}
%
\newcommand{\Selfish}{\ensuremath{\mathrm{Selfish}}}
\newcommand{\RandTopM}{\ensuremath{\mathrm{RandTopM}}}
\newcommand{\MCTopM}{\ensuremath{\mathrm{MCTopM}}}

\newcommand{\TDFS}{\ensuremath{\mathrm{TDFS}}}
\newcommand{\MEGA}{\ensuremath{\mathrm{MEGA}}}
\newcommand{\MusicalChair}{\ensuremath{\mathrm{Musical}\,\mathrm{Chair}}}
\newcommand{\SICMMAB}{\ensuremath{\mathrm{SIC}}-\ensuremath{\mathrm{MMAB}}}

% Abbreviations
\newcommand{\Mbest}{\ensuremath{M\text{-}\mathrm{best}}}
\newcommand{\Mworst}{\ensuremath{M\text{-}\mathrm{worst}}}
\newcommand{\TopM}{\widehat{M^j}}

\newcommand{\limInf}{\underline{\lim}}
