Add q-learning and improve value iteration pseudocode

source-code/Pseudocode/Value-Iteration/Value-Iteration.tex

@@ -23,8 +23,8 @@
         \Statex Actions $\mathcal{A} = \{1, \dots, n_a\},\qquad A: \mathcal{X} \Rightarrow \mathcal{A}$
         \Statex Cost function $g: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$
         \Statex Transition probabilities $f$
-        % TODO: \alpha?
-        \Procedure{ValueIteration}{$\mathcal{X}$, $A$, $g$, $f$}
+        \Statex Learning rate $\alpha \in [0, 1]$, typically $\alpha = 0.1$
+        \Procedure{ValueIteration}{$\mathcal{X}$, $A$, $g$, $f$, $\alpha$}
             \State Initialize $J, J': \mathcal{X} \rightarrow \mathbb{R}_0^+$ arbitrarily
             \While{$J$ is not converged}
                 \State $J' \gets J$
@@ -37,9 +37,10 @@
                     \State $J(x) \gets \min_a \{Q(x, a)\}$
                 \EndFor
             \EndWhile
+            \Return $J$
         \EndProcedure
         \end{algorithmic}
-    \caption{Value Iteration}
+    \caption{Value Iteration: Learn function $J: \mathcal{X} \rightarrow \mathbb{R}$}
     \label{alg:value-iteration}
     \end{algorithm}
 \end{preview}

source-code/Pseudocode/q-learning/Makefile

@@ -0,0 +1,36 @@
+SOURCE = q-learning
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	make
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg
+	rsvg-convert -a -w $(WIDTH) -f svg $(SOURCE).svg -o $(SOURCE)2.svg
+	inkscape $(SOURCE)2.svg --export-plain-svg=$(SOURCE).svg
+	rm $(SOURCE)2.svg

source-code/Pseudocode/q-learning/README.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](q-learning.png)

source-code/Pseudocode/q-learning/q-learning.tex

@@ -0,0 +1,45 @@
+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
+\usepackage{braket} % needed for \Set
+\usepackage{caption}
+\usepackage{algorithm}
+\usepackage[noend]{algpseudocode}
+
+\DeclareCaptionFormat{myformat}{#3}
+\captionsetup[algorithm]{format=myformat}
+
+\begin{document}
+\begin{preview}
+    \begin{algorithm}[H]
+        \begin{algorithmic}
+        \Require
+        \Statex Sates $\mathcal{X} = \{1, \dots, n_x\}$
+        \Statex Actions $\mathcal{A} = \{1, \dots, n_a\},\qquad A: \mathcal{X} \Rightarrow \mathcal{A}$
+        \Statex Reward function $R: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$
+        \Statex Black-box (probabilistic) transition function $T: \mathcal{X} \times \mathcal{A} \rightarrow \mathcal{X}$
+        \Statex Learning rate $\alpha \in [0, 1]$, typically $\alpha = 0.1$
+        \Statex Discounting factor $\gamma \in [0, 1]$
+        \Procedure{QLearning}{$\mathcal{X}$, $A$, $R$, $T$, $\alpha$, $\gamma$}
+            \State Initialize $Q: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$ arbitrarily
+            \State Start in state $s \in \mathcal{X}$
+            \While{$Q$ is not converged}
+                \State Select $a \in \mathcal{A}$ by $Q$ and an exploration policy (e.g. $\varepsilon$ greedy)
+                \State $r \gets R(s, a)$
+                \State $s' \gets T(s, a)$ \Comment{Receive the new state}
+                \State $Q(s', a) \gets (1 - \alpha) \cdot Q(s, a) + \alpha \cdot (r + \gamma \cdot \max_{a'} Q(s', a'))$
+                \State $s \gets s'$
+            \EndWhile
+            \Return $Q$
+        \EndProcedure
+        \end{algorithmic}
+    \caption{$Q$-learning: Learn function $Q: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$}
+    \label{alg:q-learning}
+    \end{algorithm}
+\end{preview}
+\end{document}