\batchmode
\documentstyle[jair,twoside,11pt,theapa]{article}
\makeatletter
\input epsf 
\ShortHeadings{Accelerating Reinforcement Learning}
{Drummond}
\firstpageno{1}


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\begin{document}
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\stepcounter{section}
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.75in\epsfbox{rooms.eps}
  \end{center} 
  
  \label{fig:rooms}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.5in\epsfbox{graph_surf_map.eps}
  \end{center} 
  
  \label{fig:mapping}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.2in\epsfbox{graph.eps}
  \end{center} 
  
  \label{fig:graph}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.5in\epsfbox{compose.eps}
  \end{center} 
  
  \label{fig:compose}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{6.5 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.65in\epsfbox{single_room.eps}
    \end{center}
    
    \label{fig:old_task}
  \end{minipage}
  \hspace{2 cm} \begin{minipage}[b]{6.5 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.65in\epsfbox{single_room2.eps}
    \end{center}
    
    \label{fig:new_task}
  \end{minipage}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{7 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.9in\epsfbox{ex6_start_func.eps}
    \end{center}
    
    \label{fig:start_func}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{7 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.9in\epsfbox{ex6_int_func.eps}
    \end{center}
    
    \label{fig:int_func}
  \end{minipage}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{7 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.9in\epsfbox{ex6_2000_func.eps}
    \end{center}
    
    \label{fig:two_func}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{7 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.9in\epsfbox{ex6_conv_func.eps}
    \end{center}
    
    \label{fig:nt_func}
  \end{minipage}
\end{figure}
}

\stepcounter{subsection}
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{7.25 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.85in\epsfbox{robot_arm.eps}
    \end{center}
    
    \label{fig:robot_arm}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.65in\epsfbox{cspace.eps}
    \end{center}
    
    \label{fig:cspace}
  \end{minipage}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.2in\epsfbox{rob_arm_surf.eps}
  \end{center}
  
  \label{fig:RL_arm}
\end{figure}
}

\stepcounter{section}
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}

{\newpage
\clearpage
\samepage \begin{equation}Q_{s,a}^{t+1}= (1-\alpha)Q_{s,a}^t + \alpha (r+\gamma max_{a'}Q_{s',a'}^t)
\label{eqn:QL}
\end{equation}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\alpha$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1778: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=6.0in\epsfbox{snake2.eps}
  \end{center} 
  
  \label{fig:fsnake}
\end{figure}
}

\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.5in\epsfbox{snake_expand2.eps}
  \end{center}
  
  \label{fig:control}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.5in\epsfbox{corner.eps}
  \end{center}
  
  \label{fig:corner}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{6 cm}
    \begin{center}
      \leavevmode\epsfxsize=3.1in\epsfbox{surf_merc3.eps}
    \end{center}
    
    \label{fig:smoothed}
  \end{minipage}
  \hspace{2 cm} \begin{minipage}[b]{6 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.65in\epsfbox{snake_merc2.eps}
    \end{center}
    
    \label{fig:mercury} 
  \end{minipage}
\end{figure}
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{\newpage
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.5in\epsfbox{snake3.eps}
  \end{center}
  
  \label{fig:forces}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{equation}x^\prime =C_0 x+C_1 y+C_2 \hspace{0.25in} y^\prime =C_3 x+C_4 y+C_5
    \label{eqn:affine}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.5in\epsfbox{lmap.eps}
  \end{center} 
  
  \label{fig:weighting}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{equation}Affine \supset Similar \supset  Symmetric
  \label{eqn:subset}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\begin{array}{llll}
error &=&  sqrt(\sum _{i}w_{i}(\Delta x_{i}^{2}+\Delta y_{i}^{2})) & \mbox{(node misalignment)}\cr
     &+&\left(\log_2\left|\frac{r_{maj}}{r_{min}}\right|\right)^2
     &\mbox{(Euclidean Distortion)} \cr
    &+&0.05\left(\log_2\left(\frac{\left|r_{maj}+r_{min}\right|}{2}\right)\right)^2 &\mbox{(scaling factor)}\cr
\end{array}
\label{eqn:error}
\end{equation}
}

{\newpage
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}

{\newpage
\clearpage
\samepage \begin{equation}v = c_1x + c_2 y + c_2 xy + c_3
\label{eqn:bilin}
\end{equation}
}

{\newpage
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.7in\epsfbox{dijkstra.eps}
  \end{center} 
  
  \label{fig:Dijkstra}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.45in\epsfbox{new_door.eps}
  \end{center} 
  
  \label{fig:new}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.65in\epsfbox{maximum.eps}
  \end{center} 
  
  \label{fig:maximum}
\end{figure}
}

{\newpage
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\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.5in\epsfbox{combining_desc.eps}
  \end{center} 
  
  \label{fig:desc}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=5.5in\epsfbox{combining_desc3.eps}
  \end{center} 
  
  \label{fig:comb}
\end{figure}
}

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x,y \rangle$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1844: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.0in\epsfbox{thesis_suites.eps}
  \end{center}
  
  \label{fig:suites}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{thesis_mgr_res.eps}
  \end{center} 
  
  \label{fig:curves_mgr}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.0in\epsfbox{thesis_mobs.eps}
  \end{center}
  
  \label{fig:two_obs}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{thesis_mga_res.eps}
  \end{center} 
  
  \label{fig:curves_mga}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.0in\epsfbox{thesis_lrooms.eps}
  \end{center}
  
  \label{fig:lrooms}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{thesis_t1r_res.eps}
  \end{center} 
  
  \label{fig:curves_srr}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=3.0in\epsfbox{thesis_sobs.eps}
  \end{center}
  
  \label{fig:one_obs}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{thesis_t1a_res.eps}
  \end{center} 
  
  \label{fig:curves_soa}
\end{figure}
}

\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
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{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{pom_curves.eps}
  \end{center} 
  
  \label{fig:pomc}
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{center}
    \leavevmode\epsfxsize=4.5in\epsfbox{thesis_mgr_minus.eps}
  \end{center} 
  \vspace*{0.025in}  
  \begin{center}
    \leavevmode\epsfxsize=3.0in\epsfbox{thesis_suites_minus.eps}
  \end{center} 
  
  \label{fig:curves_fmgr}
\end{figure}
}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.85in\epsfbox{room3dw.eps}
    \end{center}
    
    \label{fig:zd}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.85in\epsfbox{room3d321.eps}
    \end{center}
    
    \label{fig:room3d321}
  \end{minipage}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.85in\epsfbox{little_car.eps}
    \end{center}
    
    \label{fig:car}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.85in\epsfbox{car_cont.eps}
    \end{center}
    
    \label{fig:car_state}
  \end{minipage}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[hbtp]
  \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=3.0in\epsfbox{car_func.eps}
    \end{center}
    
    \label{fig:car_func}
  \end{minipage}
  \hspace{1 cm} \begin{minipage}[b]{6.75 cm}
    \begin{center}
      \leavevmode\epsfxsize=2.5in\epsfbox{car_snake4.eps}
    \end{center}
    
    \label{fig:csnake}
  \end{minipage}
\end{figure}
}

\stepcounter{section}
\stepcounter{section}
\appendix
{\newpage
\clearpage
\samepage \begin{equation}E_{spline}(\hat{f})=\int _{R}\left( E_{fit}(\hat{f})+E_{smooth}(\hat{f})\right) ds
\label{eqn:energy}
\end{equation}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\omega_{t}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1860: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\omega_{s}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1862: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{equation}-\frac{\partial }{\partial s} (\omega_{t}(s)\frac{\partial \hat{f}(s)}{\partial s})
  +\frac{\partial } {\partial s^{2}}(\omega _{s}(s)\frac{\partial
    ^{2}\hat{f}(s)}{\partial   s^{2}})
  =f_{in}(s)-\hat{f}(s) 
\label{eqn:euler_spline}
\end{equation}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$Q_{max}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1878: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{equation}\mu \frac{\partial ^{2}\hat{f}}{\partial t^{2}}+\gamma \frac{\partial \hat{f}}{\partial t}
  + {\frac{\partial }{\partial t} \left(\frac{\partial }{\partial s^{2}}\left(\omega _{c}(s)\frac{\partial^{2}\hat{f}}{\partial s^{2}}\right)\right)
  +\frac{\partial }{\partial s^{2}}\left(\omega
    _{tp}(s)\frac{\partial^{2}\hat{f}}{\partial
      s^{2}}\right)}
  = F(\hat{f})
  \label{eqn:euler_snake}
\end{equation}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\omega _{c}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1880: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\mu$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1884: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{equation}F(\hat{f}) = M(\hat{f})\overrightarrow{n}(s)+ \nabla (-\left|
    \nabla Q_{max}(\hat{f})\right|^2)\overrightarrow{n}(s)
  \label{eqn:normal}
\end{equation}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\nabla \left|Q_{max}\right|^2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1892: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{equation}-\frac{\partial \left| \nabla Q_{max}\right|^2}{\partial x}
  =-2\left[(\frac{\partial Q_{max}}{\partial x})(\frac{\partial
      ^{2}Q_{max}}{\partial x^2})
    +(\frac{\partial Q_{max}}{\partial
      y})(\frac{\partial ^{2}Q_{max}}{\partial x \partial y})\right]
  \label{eqn:Qenergy}
\end{equation}
}

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\stepcounter{section}

\end{document}
