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Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables. Computing the maximum expected utility (MEU) and the optimizing policy is exponential in the constrained induced width and therefore is notoriously difficult for larger models. In this paper, we develop a new bounding scheme for MEU that applies partitioning based approximations on top of the decomposition scheme called a multi-operator cluster DAG for influence diagrams that is more sensitive to the underlying structure of the model than the classical join-tree decomposition of influence diagrams. Our bounding scheme utilizes a cost-shifting mechanism to tighten the bound further. We demonstrate the effectiveness of the proposed scheme on various hard benchmarks. 

Influence diagrams (IDs) are graphical models for representing and reasoning with sequential decision-making problems under uncertainty. Limited memory influence diagrams (LIMIDs) model a decision-maker (DM) who forgets the history in the course of making a sequence of decisions. The standard inference task in IDs and LIMIDs is to compute the maximum expected utility (MEU), which is one of the most challenging tasks in graphical models. We present a model decomposition framework in both IDs and LIMIDs, which we call submodel decomposition that generates a tree of single-stage decision problems through a tree clustering scheme. We also develop a valuation algebra over the submodels that leads to a hierarchical message passing algorithm that propagates conditional expected utility functions over a submodel-tree as external messages. We show that the overall complexity is bounded by the maximum tree-width over the submodels, common in graphical model algorithms. Finally, we present a new method for computing upper bounds over a submodel-tree by first exponentiating the utility functions yielding a standard probabilistic graphical model as an upper bound and then applying standard variational upper bounds for the marginal MAP inference, yielding tighter upper bounds compared with state-of-the-art bounding schemes for the MEU task. 

An influence diagram is a graphical representation of sequential decision-making under uncertainty, defining a structured decision problem by conditional probability functions and additive utility functions over discrete state and action variables. The task of finding the maximum expected utility of influence diagrams is closely related to the cost-optimal probabilistic planning, stochastic programmings, or model-based reinforcement learning. In this position paper, we address the heuristic search for solving influence diagram, where we generate admissible heuristic functions from graph decomposition schemes. Then, we demonstrate how such heuristics can guide an AND/OR branch and bound search. Finally, we briefly discuss the future directions for improving the quality of heuristic functions and search strategies.