\usepackage{bm,bbm,amsmath,amsfonts,amssymb}
\usepackage{xspace}
\usepackage{eucal} 

\def\defeq{\doteq}
\def\Re{\mathbb{R}}
\def\cross{\times}
\def\grad{\nabla}
\def\first#1#2{\frac{\partial #1}{\partial #2}}
\def\second#1#2{\frac{\partial^2 #1}{\partial #2^2}}
\def\p(#1|#2){p(#1\,|\,#2)}
\def\w{{\bf w}}
\def\x{{\bf x}}
\def\v{{\bf v}}
\def\z{{\bf z}}
\def\th{{\bm\theta}}
\newcommand{\EE}[2]{\mathbb{E}_{#1\!\!}\left[#2\right]}
\newcommand{\CEE}[3]{\EE{#1}{{#2}~\middle\vert~{#3}}}
\def\E#1{\EE{\,}{#1}}
\def\CE#1#2{\CEE{\,}{#1}{#2}}
\def\CP#1#2{\Pr{#1\mid#2}}
\def\Pr#1{{{\rm Pr\!}\left\{#1\right\}}}
\def\g{\mbox{$\gamma$}\xspace}
\def\a{\mbox{$\alpha$}\xspace}
\def\l{\mbox{$\lambda$}\xspace}
\def\e{\mbox{$\varepsilon$}\xspace}
\def\ee{\mbox{$\varepsilon$}\xspace}
\def\={\!=\!}
\def\X{{\cal X}}
\def\Y{{\cal Y}}
\def\A{{\cal A}}
\def\S{{\cal S}}
\def\P{{\cal P}}
\def\R{{\cal R}}
\def\O{{\cal O}}
\def\tr{^\top}
\def\simc{\!\sim\!}
\def\ind#1{{\mathbbm 1}_{#1}}
\def\la{($\lambda$)\xspace}
\def\vpi{v_\pi}
\def\vstar{v_*}
\def\qpi{q_\pi}
\def\qstar{q_*}
\newcommand{\norm}[1]{\left\Vert#1\right\Vert^2_{\mu}}
\newcommand{\size}[1]{\lvert#1\rvert}
\def\MSBEm{\overline{\text{BE}}}
\def\MSBE{$\overline{\text{BE}}$\xspace}
\def\MSPBEm{\overline{\text{PBE}}}
\def\MSPBE{$\overline{\text{PBE}}$\xspace}
\def\MSTDEm{\overline{\text{TDE}}}
\def\MSTDE{$\overline{\text{TDE}}$\xspace}
\def\MSREm{\overline{\text{RE}}}
\def\MSRE{$\overline{\text{RE}}$\xspace}
\def\MSVEm{\overline{\text{VE}}}
\def\MSVE{$\overline{\text{VE}}$\xspace}

