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