Optimal Cybersecurity Investments in Large Networks Using SIS Model: Algorithm Design

We study the problem of minimizing the (time) average security costs in large networks/systems comprising many interdependent subsystems, where the state evolution is captured by a susceptible-infected-susceptible (SIS) model. The security costs reflect security investments, economic losses and recovery costs from infections and failures following successful attacks. We show that the resulting optimization problem is nonconvex and propose a suite of algorithms - two based on a convex relaxation, and the other two for finding a local minimizer, based on a reduced gradient method and sequential convex programming. Also, we provide a sufficient condition under which the convex relaxations are exact and, hence, their solution coincides with that of the original problem. Numerical results are provided to validate our analytical results and to demonstrate the effectiveness of the proposed algorithms.