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Reorganize paths to figures
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nianze committed May 18, 2021
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102 changes: 51 additions & 51 deletions Talks/oral_defense/dependency-ssat/dec-pomdp.tex
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@@ -1,59 +1,59 @@
\begin{frame}
\frametitle{Modeling Decentralized POMDP}
\begin{itemize}
\item Multiple agents with uncertainty and partial information~\cite{Oliehoek2016}
\pause
\item NEXPTIME-completeness~\cite{Bernstein2002}
\pause
\item $\mathcal{M} = (I,S,\{A_i\},$ $T, \rho, \{O_i\}, \Omega, \Delta_0, h)$
\pause
\begin{itemize}
\item $T: S \times (A_1 \times \cdots \times A_n) \times S \mapsto [0,1]$
\pause
\item $\rho: S \times (A_1 \times \cdots \times A_n) \mapsto \mathbb{R}$
\pause
\item $\Omega: S \times (A_1 \times \cdots \times A_n) \times (O_1 \times \cdots \times O_n) \mapsto [0,1]$
\pause
\end{itemize}
\item Optimal \emph{joint policy} to maximize the expected total reward
\pause
\item A polynomial-time reduction from Dec-POMDP to DSSAT
\pause
\begin{itemize}
\item Extending the reduction from POMDP to SSAT~\cite{Salmon2020}
\end{itemize}
\end{itemize}
\frametitle{Modeling Decentralized POMDP}
\begin{itemize}
\item Multiple agents with uncertainty and partial information~\cite{Oliehoek2016}
\pause
\item NEXPTIME-completeness~\cite{Bernstein2002}
\pause
\item $\mathcal{M} = (I,S,\{A_i\},$ $T, \rho, \{O_i\}, \Omega, \Delta_0, h)$
\pause
\begin{itemize}
\item $T: S \times (A_1 \times \cdots \times A_n) \times S \mapsto [0,1]$
\pause
\item $\rho: S \times (A_1 \times \cdots \times A_n) \mapsto \mathbb{R}$
\pause
\item $\Omega: S \times (A_1 \times \cdots \times A_n) \times (O_1 \times \cdots \times O_n) \mapsto [0,1]$
\pause
\end{itemize}
\item Optimal \emph{joint policy} to maximize the expected total reward
\pause
\item A polynomial-time reduction from Dec-POMDP to DSSAT
\pause
\begin{itemize}
\item Extending the reduction from POMDP to SSAT~\cite{Salmon2020}
\end{itemize}
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Modeling Decentralized POMDP}
\begin{center}
\input{fig/formulas.tex}
\end{center}
\frametitle{Modeling Decentralized POMDP}
\begin{center}
\input{fig/dependency-ssat/dec-pomdp-formulas.tex}
\end{center}
\end{frame}

\begin{frame}
\frametitle{Modeling Decentralized POMDP}
\begin{itemize}
\item Policy selection for a single agent~\cite{Salmon2020}
\pause
\begin{itemize}
\item
$\exists x_a^{i,0},\random{} x_p^0,\random{} x_o^{i,0},\ldots,\exists x_a^{i,h-2},\random{} x_p^{h-2},\random{} x_o^{i,h-2},\exists x_a^{i,h-1},\random{} x_p^{h-1}$
\end{itemize}
\pause
\item Joint policy for multiple agents
\pause
\begin{itemize}
\item An agent can only base its actions on \alert{its own observations}
\pause
\item A linearly ordered prefix for all agents?
\end{itemize}
\pause
\item Explicitly specify dependency sets in DSSAT
\pause
\begin{itemize}
\item $D_{x_a^{i,t}}=\{x_o^{i,0},\ldots,x_o^{i,t-1},x_p^0,\ldots,x_p^{t-1}\}$
\end{itemize}
\end{itemize}
\frametitle{Modeling Decentralized POMDP}
\begin{itemize}
\item Policy selection for a single agent~\cite{Salmon2020}
\pause
\begin{itemize}
\item
$\exists x_a^{i,0},\random{} x_p^0,\random{} x_o^{i,0},\ldots,\exists x_a^{i,h-2},\random{} x_p^{h-2},\random{} x_o^{i,h-2},\exists x_a^{i,h-1},\random{} x_p^{h-1}$
\end{itemize}
\pause
\item Joint policy for multiple agents
\pause
\begin{itemize}
\item An agent can only base its actions on \alert{its own observations}
\pause
\item A linearly ordered prefix for all agents?
\end{itemize}
\pause
\item Explicitly specify dependency sets in DSSAT
\pause
\begin{itemize}
\item $D_{x_a^{i,t}}=\{x_o^{i,0},\ldots,x_o^{i,t-1},x_p^0,\ldots,x_p^{t-1}\}$
\end{itemize}
\end{itemize}
\end{frame}
2 changes: 1 addition & 1 deletion Talks/oral_defense/dependency-ssat/prob-approx-design.tex
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Expand Up @@ -12,7 +12,7 @@
\pause
\begin{figure}
\centering
\includegraphics[scale=0.6]{fig/dssat-prob-miter.pdf}
\includegraphics[scale=0.6]{fig/dependency-ssat/dssat-prob-miter.pdf}
\end{figure}
\pause
\begin{align*}
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2 changes: 1 addition & 1 deletion Talks/oral_defense/prob-design-eval/modeling.tex
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Expand Up @@ -32,7 +32,7 @@
\pause
\begin{figure}
\centering
\includegraphics[scale=0.8]{fig/prob-distillation.pdf}
\includegraphics[scale=0.8]{fig/prob-design-eval/prob-distillation.pdf}
\end{figure}
\end{block}
\pause
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2 changes: 1 addition & 1 deletion Talks/oral_defense/prob-design-eval/solutions.tex
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Expand Up @@ -3,7 +3,7 @@
\begin{block}{Property Violation Probability}
\begin{figure}
\centering
\includegraphics[scale=0.8]{fig/prob-spbn-miter.pdf}
\includegraphics[scale=0.8]{fig/prob-design-eval/prob-spbn-miter.pdf}
\end{figure}
\pause
\begin{itemize}
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