Rotecting national infrastructure such as airports, historical
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C x l i X ij l i ≥ ∈ ∑ adversary type ob serves the LAWA police check- point policy and then decides where to attack. Since adversaries can observe the LAWA police pol- icy before deciding their actions, this can be mod- eled through a Stackelberg game with the police as the leader. In this setting, the set X of possible actions for LAWA po lice is the set of possible checkpoint com- binations. If, for instance, LAWA police were set- ting up one checkpoint then X = {1, ..., k}. If LAWA police were setting up a combi nation of two check- points, then X = {(1, 2), (1, 3)...(k − 1, k)}, that is, all combinations of two checkpoints. Each adver sary type l ∈ L = {1, ..., m} can decide to attack one of the k roads or maybe not attack at all (none), so its set of ac tions is Q = {1, …, k, none}. If LAWA police select road i to place a checkpoint on and adver- sary type l ∈ L selects road j to attack then the police receive a reward R l ij and the adversary receives a reward C l ij . These reward values vary based on three considerations: the chance that the LAWA police checkpoint will catch the adversary on a particular inbound road; the damage the adversary will cause if it attacks by means of a par- ticular inbound road; and the type of adversary, that is, adversary capability. If LAWA police catch the adver sary when i = j, we make R l ij a large posi- tive value and C l ij a large negative value. However, the probability of catching the adversary at a checkpoint is based on the volume of traf fic through the checkpoint (significant traffic will increase the difficulty of catching the adversary), which is an input to the system. If the LAWA police are unable to catch the ad versary, then the adver- sary may succeed; that is, we make R l ij a large nega- tive value and C l ij a large positive value. Cer tainly, if the adversary attacks from an inbound road where no checkpoint was set up, there is no chance that the po lice will catch the adversary. The mag- nitude of R l ij and C l ij vary based on the adversary’s potential target, given the road from which the adversary attacks. Some roads lead to higher val- ued targets for the adversary than others. The game is not a zero sum game, however, as even if the adversary is caught, the adversary may benefit due to publicity. The reason we consider a Bayesian Stackelberg game is because LAWA police face multiple adver- sary types. Thus, differing values of the reward matrices across the different adversary types l ∈ L represent the different objectives and valuations of the different attackers (for example, smugglers, crimi nals, terrorists). For example, a hard-core, well-financed ad versary could inflict significant damage on LAX; thus, the negative rewards to the LAWA police are much higher in magnitude than an amateur attacker who may not have suffi cient resources to carry out a large-scale attack. If these are the only two types of adversaries faced, then a Articles 48 AI MAGAZINE 20-80 split of probability implies that while there is a 20 percent chance that the LAWA police face the former type of adversary, there is an 80 percent chance that they face an amateur attacker. Our ex - perimental data provides initial results about the sensitivity of our algorithms to the probability dis- tributions over these two different adversary types. While the number of adver sary types has varied based on inputs from LAWA police, for any one adversary type the largest game that has been con- structed, which was done for canine deployment, consisted of 784 actions for the LAWA police (when multiple canine units were active) for the eight possible terminals within the airport and 8 actions per adversary type (one for a possible attack on each terminal). System Architecture There are two separate versions of ARMOR, ARMOR-checkpoint and ARMOR-canine. While in the following we focus on ARMOR-checkpoint for illustration, both these versions use the same underlying architecture with different inputs. As shown in figure 6, this architecture consists of a front end and a back end, integrating four key components: a front-end interface for user interac- tion; a method for creating Bayesian Stackelberg game matrices; an im plementation of DOBSS; and a method for producing sug gested schedules for the user. They also contain two major forms of external input. First, they allow for direct user input into the system through the interface. Sec- tải về 0.64 Mb. Chia sẻ với bạn bè của bạn:
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