Reinforcement learning algorithms for adaptive cyber defense against heartbleed

In this paper, we investigate a model where a defender and an attacker simultaneously and repeatedly adjust the defenses and attacks. Under this model, we propose two iterative reinforcement learning algorithms which allow the defender to identify optimal defenses when the information about the attacker is limited. With probability one, the adaptive reinforcement learning algorithm converges to the best response with respect to the attacks when the attacker diminishingly explores the system. With a probability arbitrarily close to one, the robust reinforcement learning algorithm converges to the min-max strategy despite that the attacker persistently explores the system. The algorithm convergence is formally proven and the algorithm performance is verified via numerical simulations.