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. Author manuscript; available in PMC: 2009 Sep 22.
Published in final edited form as: J Artif Intell Res. 2008 Jul 1;32(2):663–704.

Figure 2.

Figure 2

An AND-OR tree constructed by the search process for a POMDP with 2 actions and 2 observations. The belief states OR-nodes are represented by triangular nodes and the action AND-nodes by circular nodes. The rewards RB(b, a) are represented by values on the outgoing arcs from OR-nodes and probabilities Pr(z|b, a) are shown on the outgoing arcs from AND-nodes. The values inside brackets represent the lower and upper bounds that were computed according to Equations 19 - 22, assuming a discount factor γ = 0.95. Also notice in this example that the action a1 in belief state b1 could be pruned since its upper bound (= 11.5) is lower than the lower bound (= 13.7) of action a2 in b1.