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

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