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50 lines
No EOL
2.3 KiB
TeX
50 lines
No EOL
2.3 KiB
TeX
\documentclass{article}
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\usepackage[pdftex,active,tightpage]{preview}
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\setlength\PreviewBorder{2mm}
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\usepackage[utf8]{inputenc} % this is needed for umlauts
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\usepackage[ngerman]{babel} % this is needed for umlauts
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\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
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\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
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\usepackage{braket} % needed for \Set
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\usepackage{caption}
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\usepackage{algorithm}
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\usepackage[noend]{algpseudocode}
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\DeclareCaptionFormat{myformat}{#3}
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\captionsetup[algorithm]{format=myformat}
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\begin{document}
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\begin{preview}
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\begin{algorithm}[H]
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\begin{algorithmic}
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\Require
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\Statex Sates $\mathcal{X} = \{1, \dots, n_x\}$
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\Statex Actions $\mathcal{A} = \{1, \dots, n_a\},\qquad A: \mathcal{X} \Rightarrow \mathcal{A}$
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\Statex Reward function $R: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$
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\Statex Black-box (probabilistic) transition function $T: \mathcal{X} \times \mathcal{A} \rightarrow \mathcal{X}$
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\Statex Learning rate $\alpha \in [0, 1]$, typically $\alpha = 0.1$
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\Statex Discounting factor $\gamma \in [0, 1]$
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\Statex $\lambda \in [0, 1]$: Trade-off between TD and MC
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\Procedure{SARSA}{$\mathcal{X}$, $A$, $R$, $T$, $\alpha$, $\gamma$, $\lambda$}
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\State Initialize $Q: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$ arbitrarily
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\While{$Q$ is not converged}
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\State Select $(s, a) \in \mathcal{X} \times \mathcal{A}$ arbitrarily
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\While{$s$ is not terminal}
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\State $r \gets R(s, a)$ \Comment{Receive the reward}
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\State $s' \gets T(s, a)$ \Comment{Receive the new state}
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\State Calculate $\pi$ based on $Q$ (e.g. epsilon-greedy)
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\State $a' \gets \pi(s')$
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\State $Q(s, a) \gets (1 - \alpha ) \cdot Q(s, a) + \alpha \cdot (r + \gamma Q(s', a'))$
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\State $s \gets s'$
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\State $a \gets a'$
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\EndWhile
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\EndWhile
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\Return $Q$
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\EndProcedure
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\end{algorithmic}
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\caption{SARSA: Learn function $Q: \mathcal{X} \times \mathcal{A} \rightarrow \mathbb{R}$}
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\label{alg:sarsa}
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\end{algorithm}
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\end{preview}
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\end{document} |