\( \newcommand{\TODO}[1]{{\color{red}TODO: {#1}}} \renewcommand{\vec}[1]{\mathbf{#1}} \newcommand{\state}{\vec{x}} \def\statet{\state_t} \def\statetp{\state_{t-1}} \def\statehist{\state_{1:t-1}} \def\statetn{\state_{t+1}} \def\obs{\meas} \def\obst{\obs_t} \def\act{a} \def\actt{\act_t} \def\acttp{\act_{t-1}} \def\acttn{\act_{t+1}} \def\Obs{\mathcal{O}} \def\ObsEnc{\Phi_o} \def\ObsProb{P_o} \def\ObsFunc{C} \def\ObsFuncFull{\ObsFunc(\statet, \actt) \rightarrow \obst} \def\ObsFuncInv{\ObsFunc^{-1}} \def\ObsFuncInvFull{\ObsFuncInv(\obst, \statetp, \actt) \rightarrow \statet} \def\StateSp{\mathcal{X}} \def\Action{\mathcal{A}} \def\TransP{P_{T}} \def\Trans{T} \def\TransFull{\Trans(\statet, \actt) \rightarrow \statetn} \def\TransObs{T_c} \def\Rew{R} \def\rew{r} \def\rewards{\vec{r}_{1:t}} \def\rewt{\rew_t} \def\rewtp{\rew_{t-1}} \def\rewtn{\rew_{t+1}} \def\RewFull{\Rew(\statet, \actt) \rightarrow \rewtn} \def\TransObsFull{\TransObs(\statet, \obst, \actt, \rewt; \theta_T) \rightarrow \statetn} \def\Value{V} \def\pit{\pi_t} \def\piDef{\pi(\acttn|\statet, \obst, \actt, \rewt; \theta_\pi) \rightarrow \pit(\acttn ; \theta_\pi)} \def\Valuet{\Value_t} \def\ValueDef{\Value(\statet, \obst, \actt, \rewt; \theta_\Value) \rightarrow \Valuet(\theta_\Value)} \def\R{\mathbb{R}} \def\E{\mathbb{E}} \newcommand{\Goal}{\mathcal{G}} \newcommand{\goalRV}{G} \newcommand{\meas}{z} \newcommand{\measurements}{\vec{\meas}_{1:t}} \newcommand{\meast}[1][t]{\meas_{#1}} \newcommand{\param}{\theta} \newcommand{\policy}{\pi} \newcommand{\graph}{G} \newcommand{\vtces}{V} \newcommand{\edges}{E} \newcommand{\st}{\state} \newcommand{\stn}{\st_{t+1}} \newcommand{\stt}{\st_t} \newcommand{\stk}{\st_k} \newcommand{\stj}{\st_j} \newcommand{\sti}{\st_i} \newcommand{\St}{\mathcal{S}} \newcommand{\Act}{\mathcal{A}} \newcommand{\acti}{\act_i} \newcommand{\lpt}{\delta} \newcommand{\trans}{P_T} \newcommand{\Q}{\qValue} \newcommand{\fwcost}{Q} \newcommand{\fw}{\fwcost} \newcommand{\qValue}{Q} \newcommand{\prew}{\Upsilon} \newcommand{\epiT}{T} \newcommand{\vma}{\alpha_\Value} \newcommand{\qma}{\alpha_\qValue} \newcommand{\prewma}{\alpha_\prew} \newcommand{\fwma}{\alpha_\fwcost} \newcommand{\maxValueBeam}{\vec{\state}_{\Value:\text{max}(m)}} \newcommand{\nil}{\emptyset} \newcommand{\discount}{\gamma} \newcommand{\minedgecost}{\fwcost_0} \newcommand{\goal}{g} \newcommand{\pos}{x} %\newcommand{\fwargs}[5]{\fw_{#4}^{#5}\left({#3}\middle|{#1}, {#2}\right)} \newcommand{\fwargs}[5]{\fw_{#4}^{#5}\left({#1}, {#2}, {#3}\right)} \newcommand{\Rgoal}{R_{\text{goal}}} \newcommand{\Loo}{Latency-1:\textgreater1} \newcommand{\Loss}{\mathcal{L}} \newcommand{\LossText}[1]{\Loss_{\text{#1}}} \newcommand{\LossDDPG}{\LossText{ddpg}} \newcommand{\LossStep}{\LossText{step}} \newcommand{\LossLo}{\LossText{lo}} \newcommand{\LossUp}{\LossText{up}} \newcommand{\LossTrieq}{\LossText{trieq}} \newcommand{\tgt}{\text{tgt}} \newcommand{\Qstar}{\Q_{*}} \newcommand{\Qtgt}{\Q_{\text{tgt}}} \newcommand{\ytgt}{y_t} % Symbols \newcommand{\ctrl}{\vec{u}} \newcommand{\Ctrl}{\mathcal{U}} \newcommand{\Data}{\mathcal{D}} \newcommand{\stdt}{\dot{\state}} \newcommand{\StDt}{\dot{\StateSp}} \newcommand{\dynSt}{f} \newcommand{\dynCt}{g} \newcommand{\bDynSt}{\bar{\dynSt}} \newcommand{\bDynCt}{\bar{\dynCt}} \newcommand{\dynAff}{F} \newcommand{\bDynAff}{\bar{\dynAff}} \newcommand{\ctrlaff}{\underline{\mathbf{\ctrl}}} \newcommand{\smallbmat}[1]{\left[\begin{smallmatrix}#1\end{smallmatrix}\right]} \newcommand{\Knl}{K} \newcommand{\knl}{\kappa} \newcommand{\bKx}{k_\state} \newcommand{\bKF}{k_\dynAff} \newcommand{\bKFu}{k_{\dynAff\ctrl}} \newcommand{\bKFx}{k_{\dynAff\state}} \newcommand{\bKFux}{k_{\dynAff\ctrl\state}} \newcommand{\covf}{\text{cov}} \newcommand{\dt}{\delta t} \newcommand{\dSt}{\stdt} \newcommand{\N}{\mathcal{N}} \newcommand{\StDat}{\mathbf{X}} \newcommand{\StDtDat}{\dot{\mathbf{X}}} \newcommand{\CtDat}{\underline{\boldsymbol{\mathcal{U}}}_{1:k}} \newcommand{\mat}[1]{{#1}} \newcommand{\Y}{\mat{Y}} \newcommand{\bY}{\bar{\Y}} \newcommand{\W}{\mat{W}} \newcommand{\V}{\mat{V}} \newcommand{\mH}{\mat{H}} \newcommand{\KH}{\Knl^\mH} \newcommand{\kH}{\knl^\mH} \newcommand{\GP}{\mathcal{GP}} \newcommand{\kDA}{\knl^\dynAff} \newcommand{\KDA}{\Knl^\dynAff} %\newcommand{\M}{\mathcal{M}} \newcommand{\kh}{\knl^{\dynAff\ctrlaff}} \newcommand{\KDat}{\mathfrak{K}} \newcommand{\kDat}{\bm{\knl}} \newcommand{\KhDat}{\KDat^{\dynAff\ctrlaff}} \newcommand{\khDADat}{\kDat^{\dynAff\ctrlaff\dynAff}} \newcommand{\khDA}{\knl^{\dynAff\ctrlaff\dynAff}} \newcommand{\dynAffDat}{\mathbf{\dynAff}} \newcommand{\grad}{\nabla} \newcommand{\Lie}{\mathcal{L}} \newcommand{\tdf}{\tilde{f}} \newcommand{\tdg}{\tilde{g}} \newcommand{\barf}{\bar{f}} \newcommand{\barg}{\bar{g}} \newcommand{\erf}{\textit{erf}} \newcommand{\etal}{et~al.} \newcommand{\CBC}{\mbox{CBC}} \newcommand{\CBCtwo}{\CBC^{(2)}} \newcommand{\CBCr}{\CBC^{(r)}} \newcommand{\Prob}{\mathbb{P}} \newcommand{\tdbff}{\bff^*_k} \newcommand{\mDynAffs}{\bfM_k} \newcommand{\bfBs}{\bfB_k} \DeclareMathOperator{\vect}{\textit{vec}} \DeclareMathOperator{\diag}{\mathbf{diag}} \DeclareMathOperator{\cov}{cov} \DeclareMathOperator{\Cov}{\mathbf{Cov}} \DeclareMathOperator{\Var}{Var} % Calligraphic fonts \newcommand{\calA}{{\cal A}} \newcommand{\calB}{{\cal B}} \newcommand{\calC}{{\cal C}} \newcommand{\calD}{{\cal D}} \newcommand{\calE}{{\cal E}} \newcommand{\calF}{{\cal F}} \newcommand{\calG}{{\cal G}} \newcommand{\calH}{{\cal H}} \newcommand{\calI}{{\cal I}} \newcommand{\calJ}{{\cal J}} \newcommand{\calK}{{\cal K}} \newcommand{\calL}{{\cal L}} \newcommand{\calM}{{\cal M}} \newcommand{\calN}{{\cal N}} \newcommand{\calO}{{\cal O}} \newcommand{\calP}{{\cal P}} \newcommand{\calQ}{{\cal Q}} \newcommand{\calR}{{\cal R}} \newcommand{\calS}{{\cal S}} \newcommand{\calT}{{\cal T}} \newcommand{\calU}{{\cal U}} \newcommand{\calV}{{\cal V}} \newcommand{\calW}{{\cal W}} \newcommand{\calX}{{\cal X}} \newcommand{\calY}{{\cal Y}} \newcommand{\calZ}{{\cal Z}} % Sets: \newcommand{\setA}{\textsf{A}} \newcommand{\setB}{\textsf{B}} \newcommand{\setC}{\textsf{C}} \newcommand{\setD}{\textsf{D}} \newcommand{\setE}{\textsf{E}} \newcommand{\setF}{\textsf{F}} \newcommand{\setG}{\textsf{G}} \newcommand{\setH}{\textsf{H}} \newcommand{\setI}{\textsf{I}} \newcommand{\setJ}{\textsf{J}} \newcommand{\setK}{\textsf{K}} \newcommand{\setL}{\textsf{L}} \newcommand{\setM}{\textsf{M}} \newcommand{\setN}{\textsf{N}} \newcommand{\setO}{\textsf{O}} \newcommand{\setP}{\textsf{P}} \newcommand{\setQ}{\textsf{Q}} \newcommand{\setR}{\textsf{R}} \newcommand{\setS}{\textsf{S}} \newcommand{\setT}{\textsf{T}} \newcommand{\setU}{\textsf{U}} \newcommand{\setV}{\textsf{V}} \newcommand{\setW}{\textsf{W}} \newcommand{\setX}{\textsf{X}} \newcommand{\setY}{\textsf{Y}} \newcommand{\setZ}{\textsf{Z}} % Vectors \newcommand{\bfa}{\mathbf{a}} \newcommand{\bfb}{\mathbf{b}} \newcommand{\bfc}{\mathbf{c}} \newcommand{\bfd}{\mathbf{d}} \newcommand{\bfe}{\mathbf{e}} \newcommand{\bff}{\mathbf{f}} \newcommand{\bfg}{\mathbf{g}} \newcommand{\bfh}{\mathbf{h}} \newcommand{\bfi}{\mathbf{i}} \newcommand{\bfj}{\mathbf{j}} \newcommand{\bfk}{\mathbf{k}} \newcommand{\bfl}{\mathbf{l}} \newcommand{\bfm}{\mathbf{m}} \newcommand{\bfn}{\mathbf{n}} \newcommand{\bfo}{\mathbf{o}} \newcommand{\bfp}{\mathbf{p}} \newcommand{\bfq}{\mathbf{q}} \newcommand{\bfr}{\mathbf{r}} \newcommand{\bfs}{\mathbf{s}} \newcommand{\bft}{\mathbf{t}} \newcommand{\bfu}{\mathbf{u}} \newcommand{\bfv}{\mathbf{v}} \newcommand{\bfw}{\mathbf{w}} \newcommand{\bfx}{\mathbf{x}} \newcommand{\bfy}{\mathbf{y}} \newcommand{\bfz}{\mathbf{z}} \newcommand{\bfalpha}{\boldsymbol{\alpha}} \newcommand{\bfbeta}{\boldsymbol{\beta}} \newcommand{\bfgamma}{\boldsymbol{\gamma}} \newcommand{\bfdelta}{\boldsymbol{\delta}} \newcommand{\bfepsilon}{\boldsymbol{\epsilon}} \newcommand{\bfzeta}{\boldsymbol{\zeta}} \newcommand{\bfeta}{\boldsymbol{\eta}} \newcommand{\bftheta}{\boldsymbol{\theta}} \newcommand{\bfiota}{\boldsymbol{\iota}} \newcommand{\bfkappa}{\boldsymbol{\kappa}} \newcommand{\bflambda}{\boldsymbol{\lambda}} \newcommand{\bfmu}{\boldsymbol{\mu}} \newcommand{\bfnu}{\boldsymbol{\nu}} \newcommand{\bfomicron}{\boldsymbol{\omicron}} \newcommand{\bfpi}{\boldsymbol{\pi}} \newcommand{\bfrho}{\boldsymbol{\rho}} \newcommand{\bfsigma}{\boldsymbol{\sigma}} \newcommand{\bftau}{\boldsymbol{\tau}} \newcommand{\bfupsilon}{\boldsymbol{\upsilon}} \newcommand{\bfphi}{\boldsymbol{\phi}} \newcommand{\bfchi}{\boldsymbol{\chi}} \newcommand{\bfpsi}{\boldsymbol{\psi}} \newcommand{\bfomega}{\boldsymbol{\omega}} \newcommand{\bfxi}{\boldsymbol{\xi}} \newcommand{\bfell}{\boldsymbol{\ell}} % Matrices \newcommand{\bfA}{\mathbf{A}} \newcommand{\bfB}{\mathbf{B}} \newcommand{\bfC}{\mathbf{C}} \newcommand{\bfD}{\mathbf{D}} \newcommand{\bfE}{\mathbf{E}} \newcommand{\bfF}{\mathbf{F}} \newcommand{\bfG}{\mathbf{G}} \newcommand{\bfH}{\mathbf{H}} \newcommand{\bfI}{\mathbf{I}} \newcommand{\bfJ}{\mathbf{J}} \newcommand{\bfK}{\mathbf{K}} \newcommand{\bfL}{\mathbf{L}} \newcommand{\bfM}{\mathbf{M}} \newcommand{\bfN}{\mathbf{N}} \newcommand{\bfO}{\mathbf{O}} \newcommand{\bfP}{\mathbf{P}} \newcommand{\bfQ}{\mathbf{Q}} \newcommand{\bfR}{\mathbf{R}} \newcommand{\bfS}{\mathbf{S}} \newcommand{\bfT}{\mathbf{T}} \newcommand{\bfU}{\mathbf{U}} \newcommand{\bfV}{\mathbf{V}} \newcommand{\bfW}{\mathbf{W}} \newcommand{\bfX}{\mathbf{X}} \newcommand{\bfY}{\mathbf{Y}} \newcommand{\bfZ}{\mathbf{Z}} \newcommand{\bfGamma}{\boldsymbol{\Gamma}} \newcommand{\bfDelta}{\boldsymbol{\Delta}} \newcommand{\bfTheta}{\boldsymbol{\Theta}} \newcommand{\bfLambda}{\boldsymbol{\Lambda}} \newcommand{\bfPi}{\boldsymbol{\Pi}} \newcommand{\bfSigma}{\boldsymbol{\Sigma}} \newcommand{\bfUpsilon}{\boldsymbol{\Upsilon}} \newcommand{\bfPhi}{\boldsymbol{\Phi}} \newcommand{\bfPsi}{\boldsymbol{\Psi}} \newcommand{\bfOmega}{\boldsymbol{\Omega}} % Blackboard Bold: \newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} \newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} \newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} \newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} \newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} \newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} \newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} \newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} \newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} \newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} \newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} \newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} \newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} \newcommand{\CBCr}{\mbox{CBC}^{(r)}} \) \( \newenvironment{proof}{\paragraph{Proof:}}{\hfill$\square$} %\newtheorem{theorem}{Theorem} %\theoremstyle{remark} %\newtheorem{lemma}{Lemma} %\newtheorem{remark}{Remark} %\theoremstyle{definition} \newtheorem{defn}{Definition} %\theoremstyle{definition} \newtheorem{exmp}{Example} \newtheorem{conj}{Conjecture} %\newtheorem{corollary}{Corollary} \newtheorem{Proposition}{Proposition} \newtheorem{ansatz}{Assumption} \newtheorem{problem}{Problem} \newcommand{\oprocendsymbol}{\hbox{$\bullet$}} \newcommand{\oprocend}{\relax\ifmmode\else\unskip\hfill\fi\oprocendsymbol} \def\eqoprocend{\tag*{$\bullet$}} \newcommand{\blue}[1]{\color{blue}{#1}} %% math functions \newcommand{\modulo}{\text{mod}} %% symbols \newcommand{\real}{\mathbb{R}} \newcommand{\integers}{\mathbb{N}} \newcommand{\complex}{\mathbb{C}} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator*{\softmax}{softmax} \DeclareMathOperator*{\Tr}{Tr} \DeclareMathOperator*{\RE}{Re} \DeclareMathOperator*{\IM}{Im} \newcommand{\trc}{\mathbf{trc}} \newcommand{\Cov}{\mathbf{Cov}} \newcommand{\floor}[1]{\lfloor #1 \rfloor} \newcommand{\ceil}[1]{\lceil #1 \rceil} \newcommand{\scaleMathLine}[2][1]{\resizebox{#1\linewidth}{!}{$\displaystyle{#2}$}} \newcommand{\ubfu}{\underline{\mathbf{u}}} \)