game theory for safety and security · game theory for safety and security arunesh sinha ....
TRANSCRIPT
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Game Theory for Safety and Security
Arunesh Sinha
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Motivation: Real World Security Issues
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Central Problem
Allocating limited security resources against an
adaptive, intelligent adversary
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Prior Work
• Stackelberg Games have been very successful in practice
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Defender-Adversary Interaction: Stackelberg Game
1,0 −3,3
−9,9 1,0
𝑝↓1 =0.75
𝑝↓2 =0.25
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• Defender moves first laying out defense
• Adversary knows the defender’s mixed strategy
• Does not know the coin flips
• Stackelberg Equilibrium: Optimal randomization
1 2 3 4 5 Day:
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Outline
Threat Screening Games
Crime Prediction using Learning in Games
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Audit games
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Screening for Threats Threat Screening Games
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Airport Passenger Screening Problem
• Transport Security Administration (TSA) screens 800 million passengers
• Dynamics Aviation Risk Management Solution (DARMS) [with USC/CREATE and Milind Tambe]
• An intelligent approach to screening passengers
Screening Effectiveness
Timely Screening
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Threat Screening Games
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Actors
• Screener (TSA)
• Adversary (e.g., terrorist)
• Benign Screenees
Threat Screening Games
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Current Screening Approach
• Two broad passengers categories
• TSA Pre and general
• Same type of screening in each category (some exceptions, e.g. children)
• Long queues
• Lot of screening time spent on benign passengers
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Proposed Solution
• Finer categories for passengers: risk levels and flight
• Randomized screening
X-Ray + Metal Detector
X-Ray + AIT
X-Ray
Metal Detector
Low Risk, Domestic
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2
90
4
11
Low Risk, International
40
10
30
20
High Risk, International
5
95
0
0
Threat Screening Games
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Actions of Players
• Defender: Allocation of screening teams to passengers
• Resource capacity constraints: For example, X-ray can be used only 40 times/hour
• Passenger flow constraints: All passengers in all categories must be screened
• Adversary: Choose a passenger category to arrive in
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Threat Screening Games
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Payoffs of Players
• Defender payoff: Measures the loss incurred from a successful attack
• Probability of attack is a function of the defender and adversary strategy
• Adversary payoff: Measures the gain from a successful attack
• Probability of attack is a function of the defender and adversary strategy
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Optimization Problem
• Maximize defender payoff (i.e., minimize loss)
• Function of defender randomized strategy and adversary best response
• Subject to
• The adversary plays a best response
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Threat Screening Games
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Technical Challenges
• Very large game: ~ 10↑41 defender actions
• The equilibrium computation is NP Hard
• Current large scale optimization approaches like Column Generation (CG) fail
• Invalid solution with compact representation (CR) approach
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Threat Screening Games
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Technical Contribution
• We propose the Marginal Guided Algorithm (MGA)
• Brown, Sinha, Schlenker, Tambe; One Size Does Not Fit All: A Game-Theoretic Approach for Dynamically and Effectively Screening for Threats [AAAI 2016]
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-4
-3
-2
-1
0
10 20 30 40 50
Scre
ener
Util
ity
Flights
MGA CG
0.1 1
10 100
1000 10000
10 20 30 40 50 Run
time
(sec
onds
)
Flights
MGA CG
Threat Screening Games
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General Model for Screening
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Threat Screening Games
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Outline
Threat Screening Games
Crime Prediction using Learning in Games
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Audit games
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Privacy Concern in HealthCare Audit Games
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What’s Going On?
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} Permissive access control regime } Trust employees to do the right thing } Malicious insiders can cause breaches
Audit Games
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• Post-hoc inspection of employee accesses to patient health records
• Detect violations
• Punish violators
• Auditing is ubiquitous and effective against insider threat
• Financial auditing, computer security auditing
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Auditing Audit Games
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Audit Game Model
𝑛 suspicious cases
Auditors
𝑘 Inspections, 𝑘≪𝑛
Adversary
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Audit Games
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• Defender chooses a randomized allocation of limited resources
• Also, chooses a punishment level
• Adversary plays his best response: chooses a misdeed to commit
• Adversary gets punished if the misdeed is caught
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Actions of Players Audit Games
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Payoff of Players
• Defender payoff includes the loss incurred from a successful breach
• Probability of breach is a function of the defender and adversary strategy
• Defender payoff includes loss from a high punishment level (Punishment is not free)
• High punishment level • Negative work environment -> loss for organization
• Immediate loss from punishment -> Suspension/Firing means loss for org.
• Adversary payoff includes the gain from a successful breach
• Probability of attack is a function of the defender and adversary strategy
• Adversary payoff includes the loss due to punishment when caught
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Optimization Problem
• Maximize defender payoff (i.e., minimize loss)
• Function of defender randomized strategy, punishment level and adversary best response
• Subject to
• The adversary plays a best response (non-linear)
• Used techniques like Second Order Cone Programs for fast computation [IJCAI 2013, AAAI 2015]
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Audit Games
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General Model for Auditing
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Punishment costs lead to tradeoff between deterrence and loss due to misdeed
Optimal inspection allocation and punishment policy can be computed efficiently
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Outline
Threat Screening Games
Crime Prediction using Learning in Games
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Audit games
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A Big Problem
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Urban Crime
In 2009 7,857,000 crime $10,994,562,000
Crime Prediction
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Challenges
• Model behavior of criminals
• What is their utility?
• Criminals are not homogenous
• Crime has spatial aspects
• Opportunity
• Real world data about frequent defender-adversary interaction available
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Predictive Policing Solution
• Our contribution [AAMAS 2015, 2016]
• Learn crime and crime evolution in response to patrolling
• Then, design optimal patrols
• Distinct from “crime predicts crime” philosophy in criminology [Chen 2004; McCue 2015]
• Deployment: Licensed to a start-up ArmorWay; deployment in University of Southern California
Crime Prediction
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0
0.5
1
Acc
urac
y
EMC2 Crime predicts crime Random
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The Role of Learning in Stackelberg Games
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Learn Adversary Behavior
Plan Optimal
Defender Strategy
Data about past
interaction
Defender Strategy
Adversary Model
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Domain Description
• Five patrol areas
• Eight hour shifts
• Crime data: number of crimes/shift/area
• Patrol data: number of officers/shift/area
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Crime Prediction
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Learning Model
• Dynamic Bayesian Network (AAMAS’15)
• Captures interaction between officers and criminals
• D: Number of defenders (known)
• X: Number of criminals (hidden)
• Y: Number of crimes (known)
• T: Step = Shift
• Expectation-Maximization with intelligent factoring
T T+1 33
Crime Prediction
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Planning
DBN (Criminal Model)
Input Defender Strategy
Output Crime Number
Search problem Search space grows exponentially with the number of steps that are planned ahead
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• DOGS algorithm (AAMAS 2015)
• Apply Dynamic Programming in the search problem
Crime Prediction
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Experimental Results
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Crime heat map without patrol
Crime heat map with random patrol
Crime heat map with optimal patrol
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Data Enables Learning in Games
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Learn Adversary Behavior
Plan Optimal
Defender Strategy
Data about past
interaction
Defender Strategy
Adversary Model
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Takeaway
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Game theory enables intelligent randomized allocation of limited security resources
against an adaptive adversary
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Thank You
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