-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
nianze
committed
May 18, 2021
1 parent
de480ef
commit d876b4d
Showing
8 changed files
with
54 additions
and
54 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -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} |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
File renamed without changes.
File renamed without changes.
File renamed without changes.
File renamed without changes.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters