Btukfyl

I created this picture

with very basic TikZ components and the code looks a bit messy, is there a more elegant way to do this? And secondly, is there a way to put dots at the stubs of the arrows in the beginning and end?

begin{tikzpicture}

draw[->] (-3.7, -0.4) %%% transition stub beginning

to [out=0,in=180] (-3.1, -0.4)

to [out=0,in=270] (-3, -0.2);



draw[->] (-3.1, -0.4) %%% to R_{t-1}

to [out=0,in=90] (-3,-0.5)

to [out=270, in=90] (-3,-1);



draw (-3,-1.2) node {(R_{t-1})};

draw (-2.9,0) node {(X_{t-1})};



draw[->] (-2.9,0.3) %%% X_{t-1} to A_{t-1}

to [out=90,in=180] (-2.8, 0.4) 

to [out=0,in=180] (-1.8,0.4)

to [out=0,in=90] (-1.7,0.2);



draw (-1.7,0) node {(A_{t-1})};



draw (-1.7, -0.3) %%% join transition 

to [out=270,in=180] (-1.6,-0.4);



draw[->] (-2.8, -0.3) %%% X_{t-1} to X_t transition

to [out=270,in=180] (-2.7, -0.4) 

to [out=0,in=180] (-0.2, -0.4)

to [out=0,in=270] (-0.1, -0.2);



draw[->] (-0.2, -0.4) %%% to R_t

to [out=0,in=90] (-0.1,-0.5)

to [out=270, in=90] (-0.1,-1);



draw (-0.1,-1.2) node {(R_t)};

draw (0,0) node {(X_t)};



draw[->] (0,0.3)  %%% X_t to A_t

to [out=90,in=180] (0.1, 0.4) 

to [out=0,in=180] (1.1,0.4)

to [out=0,in=90] (1.2,0.2); 



draw (1.2,0) node {(A_t)};



draw (1.2, -0.3) %%% join transition

to [out=270,in=180] (1.3,-0.4);



draw[->] (0.1, -0.3) %%% X_t to X_{t+1} transition

to [out=270,in=180] (0.2, -0.4) 

to [out=0,in=180] (2.5, -0.4)

to [out=0,in=270] (2.6, -0.2);



draw[->] (2.5, -0.4) %%% to R_{t+1}

to [out=0,in=90] (2.6,-0.5)

to [out=270, in=90] (2.6,-1);



draw (2.6,-1.2) node {(R_{t+1})};

draw (2.7,0) node {(X_{t+1})};



draw[->] (2.7,0.3)  %%% X_{t+1} to A_{t+1}

to [out=90,in=180] (2.8, 0.4) 

to [out=0,in=180] (3.8,0.4)

to [out=0,in=90] (3.9,0.2); 



draw (3.9,0) node {(A_{t+1})};



draw (3.9, -0.3) %%% join transition stub

to [out=270,in=180] (4,-0.4);



draw (2.8, -0.3) %%% X_{t+1} transition stub end

to [out=270,in=180] (2.9, -0.4) 

to [out=0,in=180] (4.8, -0.4);



end{tikzpicture}

EDIT: Regarding the question, whether or not the arrows are supposed to overlap:

Yes, it symbolizes a transition kernel, which takes the state X_t and action A_t as input and returns the next state and reward R_{t + 1}. I also added a dotted line in the top bit, because the actions can depend on the entire history in general, although the markovian behaviors are more important.

Don't worry about updating your answers. I just wanted to learn about ways to improve next time. You helped me a ton.

Since you asked is there a more elegant way to do this, here is a starting point to define the nodes using foreach.

documentclass[margin=2mm]{standalone}

usepackage{tikz}

begin{document}

begin{tikzpicture}[%

  node distance=1.5cm,

  inner sep=2pt,

]



foreach [count=i] l in {-1,,+1}{

  node               (Xi) at (4*i,0) {$X_{tl}$};

  node[right of=Xi] (Ai)             {$A_{tl}$};

  node[below of=Xi] (Ri)             {$R_{tl}$};

}

node[left of=X1]     (left)            {phantom{$X_t$}};

node[right of=A3]    (right)           {phantom{$X_t$}};



%% dashed line

draw[dashed] ([yshift=7.5pt]left.north) -- ([yshift=7.5pt]right.north);



begin{scope}[%

  ->,

  rounded corners=5pt,

  thick,

]



%% X to A

foreach i in {1,2,3}{%

  draw (Xi.north)

     -- ([yshift=7pt]Xi.north)

     -| (Ai.north);

}



%% X to X

draw ([xshift=4pt]X1.south) -- ([xshift=4pt,yshift=-7pt]X1.south)

   -| ([xshift=-4pt]X2.south);

draw ([xshift=4pt]X2.south) -- ([xshift=4pt,yshift=-7pt]X2.south)

   -| ([xshift=-4pt]X3.south);



%% X to dots

draw ([xshift=4pt]X3.south) -- ([xshift=4pt,yshift=-7pt]X3.south)

   -- ([yshift=-7pt]right.south)node[right]{$dots$};



%% A to dots

draw (A3.south) -- ([yshift=-7pt]A3.south)

   -- ([yshift=-7pt]right.south);



%% A to R

draw (A1)

   -- ([yshift=-7pt]A1.south)

   -| (R2.north);

draw (A2)

   -- ([yshift=-7pt]A2.south)

   -| (R3.north);



%% dots to X

draw ([yshift=-7pt]left.south)node[left]{$dots$}

   -| ([xshift=-4pt]X1.south);



%% dots to R

draw ([yshift=-7pt]left.south)

   -| (R1.north);

end{scope}



end{tikzpicture}

end{document}

I improved it by using node and taking advantage of these nodes' .south and .north – this would make the texts have a better spacing with the arrows. Also, a variant of the format of the arrows is used.

documentclass[tikz,margin=3mm]{standalone}

usetikzlibrary{calc}

begin{document}

begin{tikzpicture}[scale=1.5]

% Nodes

node (rt-1) at (0,0) {$R_{t-1}$};

node (xt-1) at (0,1) {$X_{t-1}$};

node (at-1) at (1,1) {$A_{t-1}$};

node (rt)   at (2.5,0) {$R_t$};

node (xt)   at (2.5,1) {$X_t$};

node (at)   at (3.5,1) {$A_t$};

node (rt+1) at (5,0) {$R_{t+1}$};

node (xt+1) at (5,1) {$X_{t+1}$};

node (at+1) at (6,1) {$A_{t+1}$};

% Beginning

draw[<-] ($(xt-1.south)+(-.1,0)$) arc (0:-90:.25cm) coordinate (bt-1);

draw[->] ($(bt-1)+(-.5,0)$) -- (bt-1) to[out=0,in=90] (rt-1.north);

% At position t - 1

draw[->] (xt-1.north) to[out=90,in=90]  (at-1.north);

draw[->] ($(xt-1.south)+(.1,0)$) arc (180:270:.25cm) coordinate (et-1) -- ($(et-1)+(1.5,0)$) to[out=0,in=90] (rt.north);

draw[<-] ($(xt.south)+(-.1,0)$) arc (0:-90:.25cm) coordinate (bt);

draw ($(et-1)+(1.5,0)$)--(bt);

draw (at-1.south) arc (180:270:.25cm);

% At position t

draw[->] (xt.north) to[out=90,in=90]  (at.north);

draw[->] ($(xt.south)+(.1,0)$) arc (180:270:.25cm) coordinate (et) -- ($(et)+(1.5,0)$) to[out=0,in=90] (rt+1.north);

draw[<-] ($(xt+1.south)+(-.1,0)$) arc (0:-90:.25cm) coordinate (bt+1);

draw ($(et)+(1.5,0)$)--(bt+1);

draw (at.south) arc (180:270:.25cm);

% At position t + 1

draw[->] (xt+1.north) to[out=90,in=90]  (at+1.north);

draw ($(xt+1.south)+(.1,0)$) arc (180:270:.25cm) coordinate (et+1) -- ($(et+1)+(1.5,0)$);

draw (at+1.south) arc (180:270:.25cm);

% The dots as you requested

draw ($(bt-1)+(-.5,0)$) node[left] {$cdots$};

draw ($(et+1)+(1.5,0)$) node[right]{$cdots$};

end{tikzpicture}

end{document}