Algorithm 3.6.

UpdateAncestors: Updates the bounds of the ancestors of all ancestors of an OR-Node

1:	Function UpdateAncestors(b′)
	Inputs: b′: An OR-Node for which we want to update all its ancestors.
	Static: bc: The current belief state of the agent.
	T: An AND-OR tree representing the current search tree.
	L: A lower bound on V *.
	U: An upper bound on V *.
2:	while b′ ≠ bc do
3:	Set (b, a) so that action a in belief b is parent node of belief node b′
4:	LT (b, a) ← RB(b, a) + γ Σz ∈ Z Pr(z|b, a)LT (τ(b, a, z))
5:	UT (b, a) ← RB(b, a) + γ Σz ∈ Z Pr(z|b, a)UT (τ(b, a, z))
6:	$z_{b,a}^T\leftarrow {\text{argmax}}_{z\in Z}{H}_T(b,a,z)H_T^{\ast }(\tau (b,a,z))$
7:	$H_T^{\ast }(b,a)\leftarrow H_T(b,a,z_{b,a}^T)H_T^{\ast }(\tau (b,a,z_{b,a}^T))$
8:	$b_T^{\ast }(b,a)\leftarrow b_T^{\ast }(\tau (b,a,z_{b,a}^T))$
9:	LT (b) ← maxa′ ∈ A LT (b, a′)
10:	UT (b) ← maxa′ ∈ A UT (b, a′)
11:	$a_b^T\leftarrow {\text{argmax}}_{a^{\prime }\in A}{H}_T(b,a^{\prime })H_T^{\ast }(b,a^{\prime })$
12:	$H_T^{\ast }(b)\leftarrow H_T(b,a_b^T)H_T^{\ast }(b,a_b^T)$
13:	$b_T^{\ast }(b)\leftarrow b_T^{\ast }(b,a_b^T)$
14:	b′ ← b
15:	end while