Simulation method for solving hybrid influence diagrams in decision making

Influence diagrams (IDs) are powerful tools for representing and solving complex decision making problems. This paper presents a simulation-based approach for solving decision making problems formulated by hybrid IDs, which involve both discrete and continuous decision and chance variables. In the proposed method, Monte-Carlo simulation is applied in both approximating the expected conditional utility and solving the optimal decision strategies. The forward Monte-Carlo method is presented for expectation calculation, and it does not require Bayesian inference as in the standard “roll-back” method. The cross-entropy method in optimization is introduced to solve the optimal strategies. The decision variables are treated as random variables, and the decision strategies are solved by recursively updating the probability density of the decision variables. Finally, we present the simulation results of a bidding problem as an illustration.