Gene

Transformation (genetics)

Engineering

Bayesian probability

Aerospace engineering

Discrete mathematics

Bayesian game

Computer security

Literature

Portfolio

Economics

Duality (order theory)

Biochemistry

Computer science

Mathematical optimization

Stackelberg competition

Operations research

Mathematics

Artificial intelligence

Financial economics

Mathematical economics

Unimodular matrix

Sequential game

Game theory

Chemistry

Dual (grammatical number)

Interdiction

Bayesian inference

Decision Support Systems

A decision support system for cyber-security is here presented. The system aims to select an optimal portfolio of security controls to counteract multi-stage attacks. The system has several components: a preventive optimisation to select controls for an initial defensive portfolio, a learning mechanism to estimate possible ongoing attacks, and an online optimisation selecting an optimal portfolio to counteract ongoing attacks. The system relies on efficient solutions of bi-level optimisations, in particular, the online optimisation is shown to be a Bayesian Stackelberg game solution. The proposed solution is shown to be more efficient than both classical solutions like Harsanyi transformation and more recent efficient solvers. Moreover, the proposed solution provides significant security improvements on mitigating ongoing attacks compared to previous approaches. The novel techniques here introduced rely on recent advances in Mixed-Integer Conic Programming (MICP), strong duality and totally unimodular matrices.

Bayesian Stackelberg games for cyber-security decision support