\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}