Online Learning in Stackelberg Security Games with Time-Varying Attack Intensities

This work investigates no-regret online learning for Repeated Stackelberg Security Games (RSSGs) against attackers with time-varying attack intensities. Standard RSSG models often assume fixed attack intensities, limiting their ability to capture evolving attack capabilities. To bridge this gap, we formalize a model in which follower numbers, types, and attack intensities can vary across rounds. We derive an exact mixed-integer linear programming oracle under optimistic tie-breaking. Under full-information feedback, combining this oracle with online learning algorithm yields expected $\mathcal{O}(\sqrt{T})$ regret against adversarial attacker sequences. Under bandit feedback, where only aggregate attack is observed, we represent the payoffs of all candidate defense strategies through a small set of basis strategies. This representation enables unbiased estimation of all candidate strategies' payoffs from a single aggregate payoff per round. Building on this representation, we combine barycentric spanner with EXP2 to achieve expected $\mathcal{O}(\sqrt{T})$ regret against adversarial sequences. This guarantee contains no additional logarithmic factors in $T$ and matches an $\Omega (\sqrt{T})$ lower bound established within our model. Numerical simulations demonstrate the effectiveness of the proposed algorithms.