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Not learning rate but discount factor
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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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\Statex Learning rate $\alpha \in [0, 1]$, typically $\alpha = 0.1$
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\Statex Discounting factor $\alpha \in (0, 1)$, typically $\alpha = 0.9$
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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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