Agent security via approximate solvers

Efficient heuristic methods are described for approximating the optimal leader strategy for security domains where threats come from unknown adversaries. These problems can be modeled as Bayes-Stackelberg games. An embodiment of the heuristic method can include defining a patrolling or security domain problem as a mixed-integer quadratic program. The mixed-integer quadratic program can be converted to a mixed-integer linear program. For a single follower (e.g., robber or terrorist) scenario, the mixed-integer linear program can be solved, subject to appropriate constraints. For embodiments applicable to multiple follower situations, the relevant mixed-integer quadratic program and related mixed-integer linear program can be decomposed, e.g., by changing the response function for the follower from a pure strategy to a weighted combination over various pure follower strategies where the weights are probabilities of occurrence of each of the follower types.