Decision circuits: a graphical representation for efficient decision analysis computation

The exact solution for many important decision analysis problems has remained intractable, despite the recent development of several related algorithms for decision analysis computation. In this dissertation, we introduce decision circuits for influence diagram evaluation, building on the advances in arithmetic circuits for belief network inference [Darwiche, 2003]. Once compiled, arithmetic circuits efficiently evaluate probabilistic queries on the belief network, and methods have been developed to exploit both the global and local structure of the network. We show that decision circuits can be constructed and compiled in a similar fashion and promise similar benefits. Decision circuits appear to be particularly useful for real-time decision making and decision situations requiring multiple evaluations and extensive sensitivity analysis. A decision circuit is a graphical representation of the maximization, addition and multiplication operators in the appropriate sequence for the evaluation of an influence diagram. We present an efficient algorithm for influence diagram evaluation using the decision circuit framework. Decision circuits can also perform sensitivity analysis to determine how the optimal solution and value change in response to changes in the model. When decision situations are represented as decision circuits, we can exploit the efficient evaluation and differentiation processes on the compiled decision circuit for all input parameters. Although the construction of optimal decision circuits remains an open problem, we demonstrate how to exploit the conditional independence revealed in the influence diagram representation. We also show how to construct even more compact and efficient decision circuits when there are separable value functions or deterministic relationships.