Optimal risk mitigation strategies for cyber contagion in networks: A hybrid deep learning method

This paper presents a novel class of cyber security models based on SIR-type formulation. Our effort is on investigating optimal impulse controls arising from a cluster owner under exogenous cyber-attacks. We utilize the SIRS model from epidemiology to represent the spread of cyber-attacks within the cluster and evaluate the impact of protective measures. Within this framework, we determine the optimal defense strategy against effective hacking by formulating and solving a stochastic control problem with optimal switching. By employing dynamic programming principles, we derive a system of quasi-variational inequalities. Due to the inherent nonlinearity and complexity, a closed-form solution is not possible. We use a hybrid deep learning method to approximate the solution by simulating the optimal protection strategies. Finally, the effectiveness of the proposed hybrid deep learning method is validated by comparing it with the deep Galerkin method.