Commitment Without Regrets: Online Learning in Stackelberg Security Games

In a Stackelberg Security Game, a defender commits to a randomized deployment of security resources, and an attacker best-responds by attacking a target that maximizes his utility. While algorithms for computing an optimal strategy for the defender to commit to have had a striking real-world impact, deployed applications require significant information about potential attackers, leading to inefficiencies. We address this problem via an online learning approach. We are interested in algorithms that prescribe a randomized strategy for the defender at each step against an adversarially chosen sequence of attackers, and obtain feedback on their choices (observing either the current attacker type or merely which target was attacked). We design no-regret algorithms whose regret (when compared to the best fixed strategy in hindsight) is polynomial in the parameters of the game, and sublinear in the number of times steps.