\newcommand{\wt}{\widetilde}
\newcommand{\wh}{\widehat}


\newcommand{\ba}{\bold{a}}
\newcommand{\bb}{\bold{b}}
\newcommand{\bc}{\bold{c}}
\newcommand{\bd}{\bold{d}}
\newcommand{\be}{\bold{e}}
\newcommand{\bof}{\bold{f}}
\newcommand{\bg}{\bold{g}}
\newcommand{\bh}{\bold{h}}
\newcommand{\bi}{\bold{i}}
\newcommand{\bj}{\bold{j}}
\newcommand{\bk}{\bold{k}}
\newcommand{\bl}{\bold{l}}
\newcommand{\bm}{\bold{m}}
\newcommand{\bn}{\bold{n}}
\newcommand{\bo}{\bold{o}}
\newcommand{\bp}{\bold{p}}
\newcommand{\bq}{\bold{q}}
\newcommand{\br}{\bold{r}}
\newcommand{\bs}{\bold{s}}
\newcommand{\bt}{\bold{t}}
\newcommand{\bu}{\bold{u}}
\newcommand{\bv}{\bold{v}}
\newcommand{\bw}{\bold{w}}
\newcommand{\bx}{\bold{x}}
\newcommand{\by}{\bold{y}}
\newcommand{\bz}{\bold{z}}
\newcommand{\bA}{\bold{A}}
\newcommand{\bB}{\bold{B}}
\newcommand{\bC}{\bold{C}}
\newcommand{\bD}{\bold{D}}
\newcommand{\oD}{\overline{D}}
\newcommand{\bE}{\bold{E}}
\newcommand{\bF}{\bold{F}}
\newcommand{\bG}{\bold{G}}
\newcommand{\bH}{\bold{H}}
\newcommand{\bI}{\bold{I}}
\newcommand{\bJ}{\bold{J}}
\newcommand{\bK}{\bold{K}}
\newcommand{\bL}{\bold{L}}
\newcommand{\bM}{\bold{M}}
\newcommand{\bN}{\bold{N}}
\newcommand{\bO}{\bold{O}}
\newcommand{\bP}{\bold{P}}
\newcommand{\bQ}{\bold{Q}}
\newcommand{\bR}{\bold{R}}
\newcommand{\bS}{\bold{S}}
\newcommand{\bT}{\bold{T}}
\newcommand{\bU}{\bold{U}}
\newcommand{\bV}{\bold{V}}
\newcommand{\bW}{\bold{W}}
\newcommand{\bX}{\bold{X}}
\newcommand{\oX}{\overline{X}}
\newcommand{\bY}{\bold{Y}}
\newcommand{\bZ}{\bold{Z}}
\newcommand{\calS}{\mathcal{S}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% definitions for hyperref %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%fix counters
%\usepackage{aliascnt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization problems    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\probmtflprimal}{\mathcal{E}_{\mbox{\tiny MTFL}}}
\newcommand{\probmtfldual}{\mathcal{C}_{\mbox{\tiny MTFL}}}
\newcommand{\probmtfldualeps}{\mathcal{C}_{\mbox{$\varepsilon$-\tiny {MTFL}}}}
\newcommand{\mtflmodprimal}{\mathcal{E}}
\newcommand{\mtflmoddual}{\mathcal{C}}
\newcommand{\mtflmoddualeps}{{\mathcal{C}_{\vareps}}}
\newcommand{\mtflmoddualmerge}{{\mathcal{S}_{\vareps}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Algorithms stuff         %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\algnewcommand\algorithmicinput{\textbf{input:}}
%\algnewcommand\Input{\item[\algorithmicinput]}
%\algnewcommand\algorithmicoutput{\textbf{output:}}
%\algnewcommand\Output{\item[\algorithmicoutput]}
%\algdef{SE}[DOWHILE]{Do}{DoWhile}{\algorithmicdo}[1]{\algorithmicwhile\ #1}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Matrix operators         %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\transp}{\mathsf{T}}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\trace}{trace}
\DeclareMathOperator*{\range}{Ran}
\DeclareMathOperator*{\kernel}{Ker}
\DeclareMathOperator*{\diag}{Diag}
\DeclareMathOperator*{\Vecm}{Vec}
\DeclareMathOperator*{\Rank}{Rank}
\DeclareMathOperator*{\Row}{Row}
\DeclareMathOperator*{\Col}{Col}
\DeclareMathOperator*{\Op}{\textbf{op}}
\DeclareMathOperator*{\nnz}{\textbf{nnz}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Norms                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\norm}[2]{\left\Vert #1 \right\Vert_{#2}}
\newcommand{\normsmall}[2]{\Vert #1 \Vert_{#2}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Statistic operators      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\probability}{\mathbb{P}}
\newcommand{\probdist}{Pr}
\DeclareMathOperator*{\expectedvalue}{\mathbb{E}}
\newcommand{\expectedvalueover}[1]{\expectedvalue\limits_{#1}}
\newcommand{\gaussdistr}{\mathcal{N}}
\newcommand{\uniformdistr}{\mathcal{U}}
\newcommand{\indvec}{J}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Algebraic Sets           %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\realnumbers}{\mathbb{R}}
\newcommand{\realnumberssdp}{\mathbb{R}_{+}}
\newcommand{\realnumbersdp}{\mathbb{R}_{++}}
\newcommand{\naturalnumbers}{\mathbb{N}}
\newcommand{\symmetricsdp}{\boldsymbol{S}^{d}_{+}}
\newcommand{\symmetricdp}{\boldsymbol{S}^{d}_{++}}
\newcommand{\symmetric}{\boldsymbol{S}^{d}}
\newcommand{\orthogonal}{\boldsymbol{O}^{d}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MDP related notation     %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\statespace}{\mathcal{X}}
\newcommand{\statespacedisc}{S}
\newcommand{\actionspace}{\mathcal{A}}
\newcommand{\transitionspace}{\mathcal{P}}
\newcommand{\transitionkernel}{P}
\newcommand{\rewardspace}{\mathcal{R}}
\newcommand{\rewardkernel}{R}
\newcommand{\epochset}{\mathcal{T}}
\newcommand{\trajspace}{\mathcal{H}}
\newcommand{\funcspace}{\mathcal{F}}
\newcommand{\dataset}{\mathcal{D}}
\newcommand{\Qfuncspace}{\mathcal{Q}}
\newcommand{\borelsetspace}{\mathcal{B}}
\newcommand{\kernelspace}{\mathcal{K}}
%\newcommand{\muset}{\boldsymbol\mu}
\newcommand{\muset}{\mu_{\pi}}
%\newcommand{\rhoset}{\boldsymbol\rho}
\newcommand{\rhoset}{\rho_{\pi}}
\newcommand{\rewardaverage}{R}
\newcommand{\rewardsample}{r}
\newcommand{\rewardsamplevec}{\br}
%\newcommand{\optbellop}{\mathcal{T}^{*}}
\newcommand{\optbellop}{\mathcal{T}}
\newcommand{\T}{\mathcal{T}}
\newcommand{\D}{\mathcal{P}}
\renewcommand{\Re}{\mathbb{R}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Short version of notation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\wrt}{w.r.t. }
%\newcommand{\defeq}{\stackrel{\mathclap{\normalfont\mbox{\tiny def}}}{=}}
\newcommand{\maxund}[1]{\max\limits_{#1}}
\newcommand{\minund}[1]{\min\limits_{#1}}
\newcommand{\vareps}{\varepsilon}
\newcommand{\bigotime}{\mathcal{O}}
%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%

%\newtheorem{theorem}{Theorem}
%\newtheorem{lemma}{Lemma}
%\newtheorem{corollary}{Corollary}
%\newtheorem{proposition}{Proposition}
%%\newtheorem{definition}{Definition}
%\newtheorem{assumption}{Assumption}
%%\newtheorem{remark}{Remark}

\newcommand{\gl}{{\sc GL}\xspace}
\newcommand{\mtfl}{{\sc MTFL}\xspace}
\newcommand{\fqi}{{\sc F$Q$I}\xspace}
\newcommand{\lassofqi}{{\sc LASSO--F$Q$I}\xspace}
\newcommand{\glfqi}{{\sc GL--F$Q$I}\xspace}
\newcommand{\flfqi}{{\sc FL--F$Q$I}\xspace}
\newcommand{\lasso}{{\sc LASSO}\xspace}



%\newaliascnt{lemma}{theorem}
%\newtheorem{lemma}[lemma]{Lemma}
%\aliascntresetthe{lemma}
%\providecommand*{\lemmaautorefname}{Lemma}
%\newaliascnt{corollary}{theorem}
%\newtheorem{corollary}[corollary]{Corollary}
%\aliascntresetthe{corollary}
%\providecommand*{\corollaryautorefname}{Corollary}
%\newaliascnt{proposition}{theorem}
%\newtheorem{proposition}[proposition]{Proposition}
%\aliascntresetthe{proposition}
%\providecommand*{\propositionautorefname}{Proposition}
%\newaliascnt{definition}{theorem}
%\newtheorem{definition}[definition]{Definition}

%\aliascntresetthe{definition}
%\providecommand*{\definitionautorefname}{Definition}
%\newaliascnt{assumption}{theorem}
%\newtheorem{assumption}[assumption]{Assumption}
%\aliascntresetthe{assumption}
%\providecommand*{\assumptionautorefname}{Assumption}


%\newenvironment{remark}[1][Remark]{\begin{trivlist}
%\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}