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\jairheading{22}{2005}{1-40}{05/05}{01/05}
\ShortHeadings{Finding Approximate POMDP Solutions Through Belief Compression}
{Roy, Gordon, \& Thrun}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2556}%
$ F^*(b)=b\cdot\ln b-\sum b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2558}%
$\displaystyle B_{F^*}(b \,\|\, U\tilde{b} ) = \sum e^{U\tilde{b}} - b\cdot U\tilde{b} + b\cdot\ln b - \sum b$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2560}%
$ \hat b = f(U\tilde b)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2562}%
$\displaystyle B_{F^*}(b \,\|\, U\tilde{b} ) = b \cdot \ln b - b \cdot \ln \hat b +
\sum \hat b - \sum b = UKL(b \,\|\, \hat{b} )
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2564}%
$ UKL$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2568}%
$ e^{U\tilde b}/\sum e^{U\tilde b}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2570}%
$ e^{U\tilde{b}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2578}%
$ ^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2580}%
$\displaystyle L(B, U, \tilde{B}) = \sum_{i=1}^{|B|} \left ( e^{U\tilde{b}_i} - b_i \cdot U\tilde{b}_i \right ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2583}%
$ \tilde B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2612}%
$\displaystyle \frac{\partial}{\partial U} L(B, U, \tilde{B})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2616}%
$\displaystyle \frac{\partial}{\partial U} e^{(U\tilde{B})} -
\frac{\partial}{\partial U} B \circ U\tilde{B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2620}%
$\displaystyle e^{(U\tilde{B})} \tilde{B}^T - B \tilde{B}^T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2624}%
$\displaystyle (e^{(U\tilde{B})} - B ) \tilde{B}^T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2627}%
$\displaystyle \frac{\partial}{\partial \tilde{B}} L(B, U, \tilde{B})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2631}%
$\displaystyle \frac{\partial}{\partial \tilde{B}} e^{(U\tilde{B})} -
\frac{\partial}{\partial \tilde{B}} B \circ U\tilde{B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2635}%
$\displaystyle U^T e^{(U\tilde{B})} - U^T B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2639}%
$\displaystyle U^T (e^{(U\tilde{B})} - B).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2641}%
$ \tilde{B}_{\cdot j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2643}%
$ j^{th}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2647}%
$ q(\tilde{B}_{\cdot j}) =
U^T(e^{(U\tilde{B}_{\cdot j})}-B_{\cdot j})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2651}%
$ q()$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2654}%
$\displaystyle \tilde{B}^{new}_{\cdot j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2658}%
$\displaystyle \tilde{B}_{\cdot j} - \frac{q(\tilde{B}_{\cdot j})}{q'(\tilde{B}_{\cdot j})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2660}%
$\displaystyle \tilde{B}^{new}_{\cdot j} - \tilde{B}_{\cdot j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2664}%
$\displaystyle -
\frac{U^T (e^{(U\tilde{B}_{\cdot j})} - B_{\cdot j})}
{q'(\tilde{B}_{\cdot j})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2666}%
$ q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2668}%
$\displaystyle x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2670}%
$ q'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2673}%
$\displaystyle \frac{\partial q}{\partial \tilde{B}_{\cdot j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2677}%
$\displaystyle \frac{\partial }{\partial  \tilde{B}_{\cdot j}}U^T (e^{(U\tilde{B}_{\cdot j})} - B_{\cdot j})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2681}%
$\displaystyle \frac{\partial }{\partial  \tilde{B}_{\cdot j}}U^T e^{(U\tilde{B}_{\cdot j})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2685}%
$\displaystyle U^T D_j U$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2687}%
$ D_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2689}%
$ \mathtt{diag}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2691}%
$\displaystyle D_j = \mathtt{diag}(e^{U \tilde{B}_{\cdot j}}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2693}%
$\displaystyle \mathtt{diag}(b) =  \begin{bmatrix}  b(s_0) & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \ldots & b(s_{|\mathcal{S}|}) \\\end{bmatrix}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2696}%
$\displaystyle (U^T D_j U) (\tilde{B}^{new}_{\cdot j} - \tilde{B}_{\cdot j})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2700}%
$\displaystyle U^T (B_{\cdot j} - e^{U\tilde{B}_{\cdot j}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2702}%
$\displaystyle U^T D_j U \tilde{B}^{new}_{\cdot j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2706}%
$\displaystyle (U^T D_j U) \tilde{B}_{\cdot j} +
U^T D_j D_j^{-1} (B_{\cdot j} - e^{U\tilde{B}_{\cdot j}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2710}%
$\displaystyle U^T D_j (U \tilde{B}_{\cdot j} +
D_j^{-1} (B_{\cdot j} - e^{U\tilde{B}_{\cdot j}}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2712}%
$\displaystyle \tilde{B}^{new}_{\cdot j} = \frac{U^T D_j (U \tilde{B}_{\cdot j} + D_j^{-1} (B_{\cdot j} - e^{U\tilde{B}_{\cdot j}})}{(U^T D_j U + 10^{-5}I_l)}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2714}%
$ I_l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2716}%
$ l \times l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2720}%
$ U_{i \cdot}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2722}%
$ i^{th}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2726}%
$\displaystyle U^{new}_{i \cdot} = \frac{(U_{i \cdot} \tilde{B} + (B_{i \cdot} - e^{U_{i \cdot}\tilde{B}})D_i^{-1}) D_i \tilde{B}^T}{(\tilde{B} D_i \tilde{B}^T + 10^{-5}I_l)}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2733}%
$ \epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}



\setlength{\parsep}{0in}%

\setlength{\parsep}{0in}


\setlength{\parskip}{0in}%

\setlength{\parskip}{0in}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2735}%
$ B = [ b_1 | \ldots |b_{|B|} ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2737}%
$ L(B, U, \tilde{B})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2743}%
$ \tilde{B}_{\cdot j} \in \tilde{B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2745}%
$ \tilde{B}_{\cdot j}^{new}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2749}%
$ U_{i \cdot} \in U$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2751}%
$ U_{i \cdot}^{new}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2755}%
$ L(B, U, \tilde{B}) > \epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2770}%
$\displaystyle x = e^{U\tilde{b}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2784}%
$ B\approx
f(U\tilde B)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2799}%
$ 4.64 \times 10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2800}%
\includegraphics[height=2in]{figs/toy-kl-epca.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2801}%
\includegraphics[height=2in]{figs/toy-example-3bases.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2802}%
\includegraphics[height=2in]{figs/toy-example-3bases.zoom1.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2803}%
\includegraphics[height=2in]{figs/toy-example-3bases.zoom2.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2807}%
$ 0.018$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2809}%
$ 2\times10^{-9}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2819}%
$ 47.7 m \times 17 m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2821}%
$ 1m \times
1m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2823}%
$ 0.02$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2040}%
\fbox{\includegraphics[height=.9in]{figs/wean.navigation.start.eps}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2044}%
\fbox{\includegraphics[height=.9in]{figs/wean.navigation.reconstruction.ps}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2826}%
\includegraphics[height=2in]{figs/robot_kl.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2835}%
$ .5m \times .5m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}



\setlength{\picheight}{1.4in}%

\setlength{\picheight}{1.4in}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2056}%
\fbox{\includegraphics[height=\picheight]{figs/longwood_example.original.ps}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2058}%
\fbox{\includegraphics[height=\picheight]{figs/longwood_example.reconstruction.ps}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap2838}%
\includegraphics[height=\picheight]{figs/longwood_kl.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2844}%
$ \approx 800$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2846}%
$ \approx 2,000$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2848}%
$ 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2850}%
$ \tilde{B}^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2852}%
$\displaystyle \tilde{B}^* = \{ \tilde{b}^*_1, \tilde{b}^*_2, \ldots,  \tilde{b}^*_{|\tilde{B}^*|}\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2854}%
$ k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2856}%
$ t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2858}%
$ V^t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2860}%
$ (t-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2862}%
$ V^{t-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2864}%
$\displaystyle V^t(\tilde{b}^*_i) = \max_a \left ( \tilde{R}^*(\tilde{b}^*_i, a) + \gamma \sum^{|\tilde{B}^*|}_{j=1}\tilde{T}^*(\tilde{b}^*_i, a, \tilde{b}^*_j)  \cdot V^{t-1}(\tilde{b}^*_j) \right )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2866}%
$ \tilde{R}^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2868}%
$ \tilde{T}^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2872}%
$ \gamma = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2879}%
$ R(s, a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2881}%
$ a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2883}%
$ s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2886}%
$\displaystyle \tilde{R}^*(\tilde{b}^*, a)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2890}%
$\displaystyle {\rm E}_{b^*} (R(s, a))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2894}%
$\displaystyle \sum^{|\mathcal{S}|}_{i=1}R(s_i, a) b(s_i).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2898}%
$ \tilde{b}^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2903}%
$ \tilde{T}^* =
p(\tilde{b}^*_j | a, \tilde{b}^*_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2907}%
$ \tilde{b}^*_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2909}%
$ \tilde{b}^*_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2913}%
$ b_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2916}%
$\displaystyle b_j(s)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2920}%
$\displaystyle \alpha
\,O(s, a, z) \sum^{|\mathcal{S}|}_{k=1} T(s_k, a, s) b_i(s_k)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2924}%
$ z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2926}%
$ T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2928}%
$ O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2940}%
$ b_a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2945}%
$\displaystyle b_a(s)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

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\end{document}
