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Join Graph Decomposition Bounds for Influence Diagrams

We introduce a new decomposition method for bounding the maximum expected utility of influence diagrams. While most current schemes use reductions to the Marginal Map task over a Bayesian Network, our approach is direct, aiming to avoid the large explosion in the model size that often results by such reductions. In this paper, we extend to influence diagrams the principles of decomposition methods that were applied earlier to probabilistic inference, utilizing an algebraic framework called valuation algebra which effectively captures both multiplicative and additive local structures present in influence diagrams. Empirical evaluation on four benchmarks demonstrates the effectiveness of our approach compared to reduction-based approaches and illustrates significant improvements in the upper bounds on maximum expected utility.