An information-theoretic and economic game framework for adversarial robustness evaluation

As deep learning algorithms are increasingly deployed, limited robustness to adversarial attacks has made security a growing concern. Existing studies often optimize attack success for a single method and rarely connect strategic behavior to economic impact, which motivates economically inspired security-game formulations that view adversarial behavior as resource allocation under realistic constraints. To address these issues, we propose KL-robust Stackelberg Economic Analysis of Risk (KLEAR), an information-theoretic security-game framework that models attacker's rational adaptation through a KL information budget and evaluates outcomes using economic utilities. We consider a sequential leader-follower interaction in which the defender commits to a system configuration and the attacker allocates probability mass over a finite set of attack options via a mixed strategy. This setup yields a closed-form KL-robust best response with a fusion interpretation, and it enables finite-horizon economic evaluation through payback and break-even analysis for deployment decisions. We then instantiate KLEAR across multiple attack scenarios and study equilibrium consequences over a range of game parameters. Extensive experiments quantify incentives on a common economic scale by accounting for fixed preparation costs and ongoing per-request gains and losses. Further, we present phase diagrams that reveal how the information budget and attack prevalence drive regime transitions in attacker composition and defender deployment. Overall, KLEAR bridges security-game theory and economic evaluation to enable systematic assessment in adversarial learning.