Counterfactual regret minimization for integrated cyber and air defense resource allocation

Abstract This research presents a new application of optimal and approximate solution techniques to solve resource allocation problems with imperfect information in the cyber and air-defense domains. We develop a two-player, zero-sum, extensive-form game to model attacker and defender roles in both physical and cyber space. We reformulate the problem to find a Nash equilibrium using an efficient, sequence-form linear program. Solving this linear program produces optimal defender strategies for the multi-domain security game. We address large problem instances with an application of the approximate counterfactual regret minimization algorithm. This approximation reduces computation time by 95% while maintaining an optimality gap of less than 3%. Our application of discounted counterfactual regret results in a further 36% reduction in computation time from the base algorithm. We develop domain insights through a designed experiment to explore the parameter space of the problem and algorithm. We also address robust opponent exploitation by combining existing techniques to extend the counterfactual regret algorithm to include a discounted, constrained variant. A comparison of robust linear programming, data-biased response, and constrained counterfactual regret approaches clarifies trade-offs between exploitation and exploitability for each method. The robust linear programming approach is the most effective, producing an exploitation to exploitability ratio of 10.8 to 1.