We show how to integrate a variable elimination approach to solving influence diagrams with a value iteration approach to solving finite-horizon partially observable Markov decision processes (POMDPs). The integration of these approaches creates a variable elimination algorithm for influence diagrams that has much more relaxed constraints on elimination order, which allows improved scalability in many cases. The new algorithm can also be viewed as a generalization of the value iteration algorithm for POMDPs that solves non-Markovian as well as Markovian problems, in addition to leveraging a factored representation for improved efficiency. The development of a single algorithm that integrates and generalizes both of these classic algorithms, one for influence diagrams and the other for POMDPs, unifies these two approaches to solving Bayesian decision problems in a way that combines their complementary advantages.
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