$$
\newcommand{\st}{\text{ s.t. }}
\newcommand{\and}{\text{ and }}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\liminf}{lim\,inf}
\DeclareMathOperator*{\limsup}{lim\,sup}
\DeclareMathOperator*{\dom}{dom}
\DeclareMathOperator*{\epi}{epi}
\newcommand{\<}{\langle}
\newcommand{\>}{\rangle}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\O}{\mathcal{O}}
\newcommand{\dist}{\text{dist}}
\newcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\diag}{\mathrm{diag}}
\newcommand{\d}{\mathrm{d}}
\newcommand{\L}{\mathcal{L}}
\newcommand{\H}{\mathcal{H}}
\newcommand{\Tr}{\mathrm{\mathbf{Tr}}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\Var}{\mathrm{Var}}
\newcommand{\Cov}{\mathrm{Cov}}
\newcommand{\indep}{\perp \!\!\! \perp}
\newcommand{\KL}[2]{\mathrm{KL}(#1 \parallel #2)}
\newcommand{\W}{\mathbf{W}} % Wasserstein distance
\newcommand{\SW}{\mathbf{SW}} % Sliced-Wasserstein distance
$$