Algorithm 3.3.

Expand subroutine of McAllester and Singh’s Algorithm.

1:	Function Expand(b, d)
	Inputs: b: The belief node we want to expand.
	d: The depth of expansion under b.
	Static: T: An AND-OR tree representing the current search tree.
	C: The number of observations to sample.
2:	if d = 0 then
3:	LT (b) ← maxa ∈ A RB(b, a)
4:	else
5:	LT (b) ← −∞
6:	for all a ∈ A do
7:	Sample = {z1, z2, … zC} from distribution Pr(z|b, a)
8:	$L_T(b,a)\leftarrow R_B(b,a)+\gamma {\sum }_{z\in Z\mid N_z(\mathcal{Z})>0}\frac{N_z(\mathcal{Z})}{C}\text{Expand}(\widehat{\tau }(b,a,z),d-1)$
9:	LT (b) ← max{LT (b), LT (b, a)}
10:	end for
11:	end if
12:	return LT (b)