Stackelberg Security Games for Security. Fernando Ordóñez Universidad de Chile

Transcription

1 Stackelberg Security Games for Security Fernando Ordóñez Universidad de Chile

2 Stackelberg Games for Security Fernando Ordóñez Universidad de Chile

3 Stackelberg Games for Security Fernando Ordóñez Milind Tambe, P. Paruchuri, C. Kiekintveld, B. An, J. Pita, M. Jain, J. Tsai, R. Yang, A. Jiang, M. Brown, E. Shieh and others

4 Stackelberg Security Game 4

5 Stackelberg Security Game 5

6 Stackelberg Security Game Monday Tuesday 6

7 Stackelberg Security Game Wednesday 7

8 Outline Stackelberg Games Deployed Applications Challenges in Stackelberg Security Games Problem Size Uncertainty/rationality Model Inputs (data, game definition) Ongoing work

9 Game Theory: Stackelberg Game Stackelberg: defender goes first, attacker second Non zero sum utilities A mixed strategy is optimal for the leader Adversary Police Target #1 Target #2 Patrol #1 7, -4-2, 3 Patrol #2-7, 7 4, -3

10 Game Theory: Stackelberg Game

11 Deployed Security Game Applications ARMOR: LAX (27) IRIS: FAMS (29) GUARDS: TSA (21) PROTECT: USCG (211)

12 Optimization Model (Rational Adversary) max x,a s.t d U ik ik ( x, q) x Total_Resources (1) x= A a A ( 2) i i T Constraint on x to enforce a feasible marginal coverage on targets j A a j j k j 1 a j 1, j (3) feasible assignment A j qk 1 qk,1 q arg max q ik U ika ( x, q ) ( 4) (5) ( 6) (7 )

13 USCG Patrols Port of Boston (Not actual areas)

14 Challenges in SSG Problem Size Uncertainty/rationality Model Inputs (data, game definition) Evaluation

15 Federal Air Marshals (FAMS) Strategy 1 Strategy 2 Strategy 3 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy 6 Strategy 1 Strategy 1 Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy 6 Strategy 2 Strategy 3

16 Multiple Defense Resources Pure strategies are joint schedules: Each air marshal assigned to a tour 4 Flights 2 Air Marshals 6 Schedules 1 Flights 1 Air Marshals 17,,,, Schedules

17 Speedup: Compact Representation ARMOR: 1 tours, 3 defenders ARMOR Actions Tour combos Prob ,2,3 1,2,4 1,2,5 8,9,1 x1 x2 x3 x12 Compact Action Tour Prob y1 y2 y3 y1 Payoff duplicates: Depends on target covered 1,2,3 1,2,4 1,3,5 Attack 1 Attack 2 Attack Attack 6 5,-1 5,-1 5,-1-2,9-2,9-2,9 4,-8 4,-8 4,-8 MILP similar to ARMOR 1 instead of 12 variables y1+y2+y3 +y1 = 3

18 Algorithm Development Tight formulations Decomposition Methods Column generation Constraint generation Heuristic Methods

19 Uncertainty/Rationality

20 Uncertainty/Rationality

21 Optimization Model (Partially Rational Adversary) Fractional and Non-Convex F ( x ) i max x,a s.t e U ia ( x ) k e d U i ( x) U a ( x ) k x Total_Resources (1) x= A a A ( 2) i T i j A a j j j j 1 a j 1, (3) feasible assignment A j ( 4)

22 Playing against Human Adversaries

23 Experimental Results PT = Prospect theory QRE = Quantal Response Equilibrium

24 Model Inputs

25 Steps to build SSG Gather representative data Define targets to protect Define time periods to protect Types of Attackers Defender and Attacker utilities

26 1: Relevant Data 2 year crime event data Horizon: annual averages of crime No daily variation No seasons Baseline patrol strategy

27 2: Targets Clustering, nodes with > 1 events in 2 meters

28 3/4: Periods/Attacker types 8 attacker types (clustering crime data) 7 Periods (cross police shifts with crime types) Prob. de un tipo de atacante en un periodo Cluster Total S1 S2 S3 S4 S5 S6 S7,234,78,32,253,23,381,516,57,18,91,27,291,624,48,18,63,22,225,142,47,26,79,48,63,49,12,66,33,238,562,79,27,93,16,223,395,97,5,15,24, Total

29 5: Utilities Crime events have a value information Cluster Promedio de Utilidad Días Reclusión Cluster Avalúo ($) $ $ $ $ $ $ $ $ $ Tasa Descuento Costo ($) % 4% 4% 4% 4% 4% 4% 4% % 38219

30 Results A frequency with which each node should be protected to maximize utilities

31 Evaluation Computer Anectdote Tests on field

32 Robustness Results: Observation Noise -,2 -,4 -,6 PASAQ(λ=1.5) -,8 DOBSS(λ= ) -1 PASAQ(noise high) -1,2 DOBSS(noise high) -1,4-1,6,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 Defender's Expected Utility Attacker λ value

33 Patrol Schedules before/after PROTECT From the Port of Boston Count Pre-PROTECT 1 5 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day Count Post-PROTECT Base Patrol Area Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

34 Adversarial Perspective Team (APT) Conduct pre- and post-protect assessment Effectiveness (tactical deterrence) increased from pre- to postprotect observations

35 On going work: protecting the border

36 Sampled patrols from optimal solution

37 Research Questions Efficient algorithms to solve real instances (patrolling on a network) Automatically determine payoff values Multiple types of security resources Validation