Decomposition Methods for Solving Finite-Horizon Large MDPs

Algorithm 2

Finding levels.

(i)	(Ω) ⟵ E; n ⟵ 0; Ln ⟵{ Ci: Ci is closed }
(ii)	If L0 = E Stop.
(iii)	Otherwise, unless Ω ≠ ∅; do
(iv)	Delete Ln (i.e., Ω ⟵ Ω/Ln and eliminate all arcs coming into Ln);
(v)	L n + 1 ⟵{ Ci: Ci is closed in the restricted MDP to Ω};
(vi)	n ⟵n + 1.