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\usepackage{color}

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\textheight 260mm
\topmargin 5mm
\textwidth 180mm
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\pagestyle{myheadings}
\markright{(Seminar in the Mathematics and Informatics Institute, Vilnius)}
\thispagestyle{empty}
\begin{document}
\begin{huge}

\clearpage  % (title) =========================================
\color{blue}
\begin{center}
{\bf Spike timing dependent plasticity (STDP) \\
\bigskip
to make robot navigation intelligent}
\hspace*{,5in}\\
\color{black}
\bigskip
\hspace*{1in}\\
\begin{Large}
Akira Imada  \\
\bigskip
Brest State Technical University (Belarus)
\end{Large}
\end{center}


\clearpage  % =========================================
\begin{center}
{\Large Topic} \\
\color{blue}
{\bf Path Planning}\\
\color{black}
{\Large or}\\
\color{blue}
{\bf Robot Navigation}\\
\color{black}
$\Downarrow$ {\Large where}\\
{\Large aim is usually to \color{red} minimize \color{black} the route from start to goal, but...}
\end{center}

%% Here I want to see it from yet another aspect.


\clearpage  % =========================================
\vspace*{.01in}
\begin{center}\color{blue}
{\bf Task of minimizing navigation \\ on its own \\ is not so difficult}\\
\bigskip
\color{black}
$\Downarrow$\\
\bigskip
{\Large A star,
Genetic Algorithm,
Reinforcement Learning,
Neural Network, \\
Ant Colony Optimization, etc...}
\end{center}

%% A star algorithme is a kind of standard approach, or GA, RL, NN are also very popular for this problem, and AC might be a good choice...



\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Genetic Algorithm (GA)}\\
\bigskip
\color{black}
{\Large
$\Downarrow$\\
\bigskip
Agent decides actions following its \color{red} chromosome\\
\color{black}
\bigskip
e.g. \\
a GA with  chromosoms like}\\
\color{black}
{\Large  (4 1 1 2 1 3 2 3 3 4 2 1 3 4 3 2 3 3 2 1 1 3 2 1 3 ...)} 
\end{center}

%% For example we can use GA with chromosomes with four different alleles each represent to north to south to east and to west



\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Random walk evolved to be minimized}\\
\end{center}
\bigskip
\begin{figure}[bhtp]
\begin{center}
   \includegraphics[width=5cm,height=6cm]{trace-96-start.eps}
   \includegraphics[width=5cm,height=6cm]{trace-96-end-new.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Task was easy}\\
%%{\bf Evolution successful}\\
%%Though number of steps grows linearly}\\
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=6cm]{evolution-96-new.eps}
%%\includegraphics[width=6cm,height=6cm]{navi-1-new.eps}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} 
{\Large Let's extend it}\\
\color{blue}
{\bf From Minimization to Maximization}\\
\bigskip
\color{black}
$\Downarrow$\\
\bigskip
{\Large Don't care goal points but to maximize an exploration}
\end{center}



\clearpage  % =========================================
\begin{center}\color{blue}
{\bf A Camel in a Desert}\\
\bigskip
\color{black}
{\LARGE
The 52nd problem \\
{\Large in the} \\
{\it ``Propositiones ad acuendos inventes''} (in Latin) \\
{\Large by} \\
Alcuin of York (732--804)}\\
\end{center}

\begin{figure}[h]
\begin{center}
%%\includegraphics[width=3cm,height=3cm]{alcuin-york.jpg}
\includegraphics[width=3cm,height=3cm]{alcuin-york.eps}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Can a camel maximize its exploration in a desert with grains on his back?}\\
\bigskip
\color{black}
\begin{figure}[bhtp]
\begin{center}
\includegraphics*[clip,width=6cm,height=4cm]{camel-test.eps}
%%\includegraphics*[clip,width=6cm,height=4cm]{camel-4.bmp}
%%includegraphics*[clip,width=6cm,height=4cm]{camel-4plus.eps}
\end{center}
\end{figure}
\end{center}


\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Modern vergion: \\From Camel to Jeep in a Desert}\\
\bigskip
\color{black}
\begin{figure}[bhtp]
\begin{center}
\includegraphics[width=10cm,height=4cm]{jeep.jpg}
\end{center}
\end{figure}
\end{center}

\clearpage  % =========================================
\vspace*{.01in}
\begin{center} \color{blue}
{\bf Can a jeep maximize its exploration \\ 
\bigskip
in a desert with a tank of fuel?}
\end{center}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Still it's not so difficult \\by GA for example}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=8cm,height=6cm]{initial.eps}
\includegraphics[width=8cm,height=6cm]{final.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Task was rather easier}\\
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=6cm,height=6cm]{random-search-needle-2.eps}
\includegraphics[width=6cm,height=6cm]{complexity.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
{\Large Let's further extend it}\\
\color{blue}
{\bf To return to the point it started}\\
\color{black}
$\Downarrow$\\
{\Large while also maximizing an exploration}
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Planet Landrover Problem}\\
\color{black}
\hspace*{1in}\\
{\Large From A (start) to B (goal) minimizing its route}\\
$\Downarrow$\\
{\Large From A to A  maximizing its route\\
\color{red}
(My proposal here as a benchmark to evaluate its intelligence of NN)}


\end{center}


\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Can the rover return to the base with its exploration being maximum?}
\bigskip
\color{black}
\begin{figure}[bhtp]
\begin{center}
\includegraphics[width=8cm,height=5cm]{mars-rover-2.jpg}
\end{center}
\end{figure}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Much more demanding}\\
\color{black}
\bigskip
$\Downarrow$\\
\bigskip
{\Large Taking GA as an example, what might be a fitness?\\
e.g.\\
{\it \{Number of crossing its previous route\} \& \{total length\}}\\
with \\
Multi Objective GA (MOGA)}
\end{center}

%% I have tried such algorithems but so far I've not succeeded


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf A Huristic Solution}\\

\bigskip
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=5cm]{max-loop-5.eps}
\end{center}
\end{figure}
\color{black}
{\Large What huristic do you guess?}
\end{center}


\clearpage  % =========================================
\vspace*{.1in}
\begin{center} 
\color{blue}
{\bf What is intelligence?}\\

\color{black}
{\Large 
$\Downarrow$ \\
Intelligence should be 
\color{red}
spontaneous, flexible, or unpredictable 
\color{black}
more or less}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Stolle et al. (2002)}\\
\hspace*{1in}\\
\color{black}
{\Large {\it ``... every day we might be cooking a different breakfast, 
but the kitchen layout is the same from day to day.''}}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf ``I beg your pardon?''}\\
\hspace*{1in}\\
\color{black}
{\Large 
Do they change the expression for an easier understanding?\\
or\\
Do they repeat the expression, maybe with a bigger voice?}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf What if your canary stop singing? \\  
{\Large Three legendary strategy in Japan.}}\\
\hspace*{1in}\\
\color{black}
{\Large 
Just wait until she sings again. \\
\bigskip
Try something so that she sings again. \\
\bigskip
Kill her if she doesn't sing any more?}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=3cm,height=3cm]{canary.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf SONY's AIBOT}
\end{center}
\bigskip
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=4cm]{aibo.jpg}
\end{center}
\end{figure}



%% synaptic plasticity 
%% floreano hebbian palastisity
%% still deterministic


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Performance is not intelligent}\\
\bigskip
\color{black}
{\Large if we use \\
\color{red}
deterministic
\color{black}
A-star, GA, NN with fixed weights?} \\
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Reinforcement Learning \\ under greedy strategy would be the one}\\
\bigskip
\color{black}
\bigskip
{\Large 
Agent follows its policy with a probability $\epsilon$ \\
and \\
choose an action at random with probability $(1-\epsilon)$ \\
\bigskip
$\Downarrow$ \\
Even after learning, actions are somehow different from run to run}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Reinforcement Learning (RL)}\\
\hspace*{1in}\\
\color{black}
{\Large
What an agent learns is a \color{red} {\it Policy}.\\
\color{black}
and \\
Policy is how to select an \color{red} {\it Action} \color{black} in the
\color{red} {\it Situation (State)} \color{black} given.\\
\bigskip
maximizing \\
the total \color{red} {\it Rewards} \color{black} it occasionary receives from the environment.
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Policy}\\
\color{black}
{\Large All possible combinations of situations and actions}
\end{center}

%% modify situation-actions prob. table by reward
%% state in our case => location + how-much-gas-remained

\clearpage  % =========================================
\hfill {\Large (cont'd)}
\begin{center}
{\Large
While in GA \\
Agent decides actions following its \color{red} chromosome\\
\color{black}
\bigskip
in RL \\
Agent decides actions following its \color{red} policy\\
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf However} \\
\bigskip
\color{black}
{\Large 
\bigskip
\color{black}
our world is with 
\color{red}
no obstacle, no wall, no corridor,
\color{black}
only one goal \\
\bigskip
$\Downarrow$ \\
Everywhere except for one point no reward nor penalty\\
\bigskip
$\Downarrow$ \\
A needle in a Heystack \\
(Rewards are not likely to be encountered by a random exploration.)}
\end{center}




\clearpage  % =========================================
\vspace*{.2in}
\begin{center} 
\color{blue}
%%{\bf Preliminary Result from this Aspect}\\
{\bf Let's make learning evolved \\ during expolration}\\
\bigskip
\color{black}
$\Downarrow$\\
{\Large Evolution of Learning}
\end{center}
%%Floreano
%%Stanley
%% eps with x, y wij with overall 4-5 neurons network


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Hebbian Learning of Reccurent NN}\\

\begin{figure}[h]
\begin{center}
\includegraphics[width=8cm,height=4cm]{plasticity.eps}
\end{center}
\end{figure}
{\Large
\color{black}
\begin{displaymath}
w_{ij}(t+1) = w_{ij}(t) + \eta x_i(t)y_j(t) 
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Floreano's approach}\\

\color{black}
$\Downarrow$\\
{\Large Modification of $w_{ij}$ during exploration}
\end{center}


\clearpage  % =========================================
\begin{center}
\color{blue}
{\bf Hebbian learning}\\   %% explain each of them  and before this page a figure
\color{black}
{\Large
\begin{displaymath}
\Delta w = (1-w)xy
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center}
\color{blue}
{\bf Hebbian type learning}\\   %% explain each of them  and before this page a figure
\color{black}
\hspace*{1in}\\
{\Large
Weaken if the postsynaptic is active, while the presynaptic is not
\begin{displaymath}
\Delta w = w(-1+x)y + (1-w)xy
\end{displaymath}
\hspace*{1in}\\
Weaken if the presynaptic is active, while the postsynaptic is not
\begin{displaymath}
\Delta w = wx(-1+y) + (1-w)xy
\end{displaymath}


\clearpage  % =========================================
%% \hfill (cont'd)\\
\hspace*{1in}\\
Strengthen if the two have similar activity and weaken otherwise.
\begin{eqnarray*}
\Delta w = \left\{
\begin{array}{ll}\nonumber
         (1-w) F(x,y)
                 & \hspace{.2in}\mbox{if}\hspace{.2in} F(x,y)>0 \\
         w F(x,y)
                 & \hspace{.2in}\mbox{otherwise}\\
         \end{array}
         \right.\\
      \end{eqnarray*}
where \\
$F(x,y) = \tanh (4(1- \vert x-y \vert) - 2)$
}
\end{center}





\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Stanley's implementation}\\
\color{black}
%%\hspace*{1in}\\
\bigskip
{\Large
$\Downarrow$\\
\begin{eqnarray*}
\Delta w = \left\{
\begin{array}{ll}\nonumber
         \eta_1 (1-w) xy + \eta_2 wx(y-1)
                 & \hspace{.2in}\mbox{for}\hspace{.1in} {\mbox {\large excitatory neuron}} \\
         - \eta_1 (1-w) xy + \eta_2 (1-w) x(1-y)
                 & \hspace{.2in}\mbox{for}\hspace{.1in} {\mbox {\large inhibitory neuron}} \\
         \end{array}
         \right.\\
      \end{eqnarray*}
$\Downarrow$ \\
Evolution of $(\eta_1, \eta_2)$ of each synaptic weight
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf More general learning}\\
\color{black}
{\Large
\begin{displaymath}
\Delta w = \eta(Axy+Bx+Cy+D)
\end{displaymath}
}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf An example of exploration \\ by a recurrent NN with random weights}\\
\end{center}

\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=5cm]{path-by-hopfield-no-learning.eps}
\end{center}
\end{figure}





\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Our Aim}\\
\bigskip
\color{black}
$\Downarrow$\\
\color{red}
{\Large Learning should occur during a random exploration\\
\color{black}
\bigskip
with \\
a spiking neural network}

%% expection to bridge between humanm & computer
%% weight modified during action
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Learning by STDP}\\
\bigskip
\color{black}
$\Downarrow$\\
{\Large The topic is still open!}
\end{center}


%% expection to bridge between humanm & computer
%% weight modified during action



\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf D. Meunier et al. (2005)}\\
\bigskip
\color{black}
$\Downarrow$\\
\color{black}
{\Large \it ``Up to now, nobody has been able to show how it is possible to learn with STDP...''}
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf M. Farries et al. (2007)}\\
\bigskip
\color{black}
$\Downarrow$\\
\color{black}
{\Large \it ``Although synaptic plasticity is widely believed to be a major component of learning, it is unclear how STDP itself could serve as a mechanism for general purpose learning.''}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Why not challenge?}
\end{center}



\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Architecture as an example}
%% A network of spike-response-model neurons with a recurrent architecture
\bigskip
\color{black}
\begin{figure}[bhtp]
\begin{center}
\includegraphics[width=8cm,height=5cm]{rnn.eps}
\end{center}
\end{figure}

$\Downarrow$ 
{\large a.k.a.\\
Echo State Network, Liquid State Network or Resevoir Computing}
\end{center}



\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Integrate-and-Fire Model}
\bigskip
\color{black}
{\Large
\begin{displaymath}
u_i(t) = u_r +(u_i(t - \delta t) - u_r) \exp (- \delta t/ \tau) + \sum_f w_{ij}f_j (t - \delta t)
\end{displaymath}
}
\end{center}
\begin{figure}[bhtp]
\begin{center}
   \includegraphics[width=14cm,height=5cm]{spike-iaf.eps}
\end{center}
\end{figure}




\clearpage  % =========================================
\begin{center} \color{blue}
{\bf What is STDP?}
\bigskip
\color{black}
{\Large
      \begin{eqnarray*}
         W(\Delta t) = \left\{
         \begin{array}{ll}\nonumber
         \hspace{.18in}A_{+} \exp (-\Delta t/\tau_{+})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t \ge 0\\
         - A_{-} \exp (-\Delta t/\tau_{-})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t < 0\\
         \end{array}
         \right.\\
      \end{eqnarray*}
where\\
$\Delta t = t_{post} - t_{pre}$
}
\end{center}






\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Reward-modulated STDP Learning}
\bigskip
\color{red}
{\Large
\begin{displaymath}
w_{ij} (t + \delta t) = w_{ij} (t) + \gamma r(t + \delta t) \zeta_{ij}(t)
\end{displaymath}
\color{black}
where
\begin{displaymath}
\zeta_{ij} (t) = P^{+}_{ij} (t)f_i(t) + P^{-}_{ij} (t)f_i(t)
\end{displaymath}
\begin{displaymath}
P^{+}_{ij} (t) = P^{+}_{ij} (t-\delta t) \exp (- \delta t/\tau_{+}) + A_{+}f_j(t)
\end{displaymath}
\begin{displaymath}
P^{-}_{ij} (t) = P^{-}_{ij} (t-\delta t) \exp (- \delta t/\tau_{-}) + A_{-}f_j(t)
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf A bigger challenging extention}\\
\bigskip
\color{black}
$\Downarrow$\\
{\Large What if the rover carries container(s) for fuel?}\\
\end{center}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Jeep Problem -- Its task}\\
\color{black}
\bigskip
{\LARGE Maximize the distance a Jeep can penetrate into 
\color{red} 1-D \color{black} desert.}
\end{center}
{\LARGE
\begin{itemize}
\item[$\bullet$] Jeep can move a unit distance with a unit fuel.
\item[$\bullet$] Jeep can unload its fuels anywhere in the desert.
\item[$\bullet$] Fuels can be filled only at the base.
\item[$\bullet$] Jeep can go back to the base \color{red} $n$ \color{black} times to re-fill its tank.
\end{itemize}
}

\clearpage  % =========================================
\begin{center}\color{blue}
%%{\bf The Solution in a 1-D desert}
{\bf An example of a success}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=18cm,height=8cm]{jeep-1d.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf An analytical  solution} \\
\bigskip
\color{black}{\Large 
by N. J. Fine (1947)
\begin{displaymath}
%% d_0 = 0, \hspace{.2in} d_n = d_{n-1}+\frac{1}{2n-1}
d_0 = 0, \hspace{.2in} d_n = d_{n-1}+1/(2n-1).
\end{displaymath}
}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=16cm,height=4cm]{jeep-1d-solution.eps}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center}\color{blue}
{\bf The optimum solution for n=3}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=18cm,height=8cm]{jeep-1d-optimum.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Conclusion}\\
\end{center}

\end{huge}
\end{document}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Candidate}\\
\color{black}
\hspace*{1in}\\
$\Downarrow$\\
\hspace*{1in}\\
%%\color{red}
{\Large Spiking Responce Model under STDP}

\end{center}

\clearpage  % =========================================
\begin{center} \color{blue}
{\bf A spiking Neuron \\--- Spiking Recponce Model (SRM)}
\bigskip
\color{black}
{\Large
\begin{displaymath}
u_i(t) = \eta_i (s_i) + \sum_j w_j \sum_f \epsilon(t - t_{j}^{f})
\end{displaymath}
}
\end{center}

%% Hodgkin-Huxley, Leaky Integrate and Fire,


\clearpage  % =========================================
\hfill {\large (Cont'd)}
\begin{center} \color{blue}
{\bf Two Kernels}
\bigskip
\color{black}
\begin{displaymath}
\epsilon(s) = \exp(-(s-d)/\tau_m)(1-exp(-s-d)/\tau_s)   
\end{displaymath}
(for $d < x < 20$ otherwise $\epsilon(s) = 0$)
\hspace*{1in}\\
\begin{displaymath}
\eta(s) = - \exp (-s/\tau_m)
\end{displaymath}
\end{center}

koko








\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Number of steps grows linearly}
\end{center}
\begin{figure}[bhtp]
\begin{center}
\includegraphics[width=14cm,height=8.5cm]{navi-1-new.eps}
\end{center}
\end{figure}



\clearpage  % =========================================
%%\hfill{\Large (cont'd)}
\begin{center}\color{blue}
{\bf The task in the modern version}\\
\color{black}
\bigskip
{\LARGE Maximize the distance a Jeep can penetrate into 
\color{red} 1-D \color{black} desert.}
\end{center}
{\LARGE
\begin{itemize}
\item Jeep can move a unit distance with a unit fuel.
\item Jeep can unload its fuels anywhere in the desert.
\item Fuels can be filled only at the base.
\item Jeep can go back to the base \color{red} $n$ \color{black} times to re-fill its tank.
\end{itemize}
}


\clearpage  % =========================================
\hspace*{1in}\\
\begin{center}\color{blue}
{\bf A success at a small scale \\is not a royal road to a real success.}
\end{center}

%% with the task being ...
\clearpage  % =========================================
\begin{center}\color{blue}
{\bf An extension to 2-D Desert}\\
\end{center}
\color{black}
\noindent
{\LARGE
\begin{center}
\color{red}``Maximize the penetration''
\color{black} or 
\color{red}``Find the needle'' \\ 
\color{black}by repeating the procedure:
\end{center}
\begin{itemize}
\item[] (1) Start the base.
\item[] (2) Navigate the desert.
\item[] (3) Put fuels somewhere, or find the fuels to get.
\item[] (4) Return to the base.
\end{itemize}
}

\clearpage  % =========================================
\begin{center}
\color{blue}{\bf Still resists to be solved!}\\
\bigskip
\color{black}{\LARGE
Evolutionary Computation \\
...... \\
Reinforcement learning \\
$\Downarrow$ \\
\color{red} An extremely tough benchmark\\
\color{black}
%%$\Downarrow$ \\
A challenge to a navigation robot community.}
\end{center}

\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Summary}
\end{center}
\color{black} {\LARGE
\begin{itemize}
\setlength{\itemsep}{0pt}
\item Two challenges:
   \begin{itemize}
   \item[$\star$] A needle hidden in a huge grid world.
                  %%{\Large (n=1 of the below)}
   \item[$\star$] \color{red}2-D Jeep Problem by a learning navigation robot.\color{black}
         \begin{itemize}
         \item[] {\Large Can a robot learn to solve this? Then how, if any?}
         \end{itemize}
     \end{itemize}
\item We have to be careful because we \\
\hspace*{0.6in}{\it tend-to-hear-what-we-want-to-hear.}
%%\item Success at a small scale is not a success in a real world.
\item Success report sometimes holds true only in a small world.


\end{itemize}
}






\end{huge}
\end{document}


