aixi.sty

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% AIXI-related formatting rules
%
% written by Jan Leike 2014
%

\usepackage{amsmath}

%---------------------------%
% Argmax and Argmin
\DeclareMathOperator*{\argmax}{arg\,max} % argmax operator
\DeclareMathOperator*{\argmin}{arg\,min} % argmin operator

%---------------------------%
% Actions, percepts, observations, and histories
\def\A{\mathcal{A}} % set of actions
\def\E{\mathcal{E}} % set of percepts
\def\H{(\A \times \E)^*} % history
\let\aechar\ae % change the name of \ae so we can redefine it
\renewcommand{\ae}{
\ifmmode\mathchoice{
	\mbox{\textsl{\aechar}}
}{
	\mbox{\textsl{\aechar}}
}{
	\mbox{\scriptsize\textsl{\aechar}}
}{
	\mbox{\scriptsize\textsl{\aechar}}
}\else\aechar\fi%
} % action-percept tuple

%---------------------------%
% Measures
\def\dmid{\parallel} % double mid
\def\leadsto{\rightarrow} % conditional probability
\newcommand{\interleaved}[2]{%
{\mathchoice{
	{\scriptscriptstyle\overleftrightarrow{\mbox{\vphantom{\footnotesize I}\normalsize${#1}\hspace{-1pt}{#2}$}}}%
}{
	{\scriptscriptstyle\overleftrightarrow{\mbox{\vphantom{\footnotesize I}\normalsize${#1}\hspace{-1pt}{#2}$}}}%
}{
	{\scriptscriptstyle\overleftrightarrow{\mbox{\vphantom{\tiny I}$\scriptstyle {#1}\hspace{-1pt}{#2}$}}}%
}{
	{\scriptscriptstyle\overleftrightarrow{\mbox{$\scriptscriptstyle {#1}\hspace{-1pt}{#2}$}}}%
}}} % agent and environment interleaved

%---------------------------%
% Expectimax operator
\usepackage{relsize}
\newcommand{\expectimax}[1]{%
\mathchoice{
	\ooalign{\hss$\max$\hss\cr$\mathlarger{\sum}\limits_{#1}$}
}{
	\ooalign{\hss$\sum$\hss\cr$\max$}_{#1}
}{}{}
}

%---------------------------%
% Deprecated macros (used in old formalism)
\def\O{\mathcal{O}} % set of observations
\def\ao{{a\hspace{-1.4pt}o}} % action-observation tuple
\def\interleave{\rightleftarrows}