Increasing Security through Communication and Policy Randomization in Multiagent Systems

1University of Southern California

Increasing Security through Communication and Policy Randomization in Multiagent Systems

Praveen Paruchuri, Milind Tambe, Fernando Ordonez

University of Southern California

Sarit Kraus

Bar-Ilan University,Israel

University of Maryland, College Park


Motivation: The Prediction Game

An UAV (Unmanned Aerial Vehicle) Flies between the 4 regions

Can you predict the UAV-fly pattern ??

Pattern 11, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,……Pattern 21, 4, 3, 1, 1, 4, 2, 4, 2, 3, 4, 3,… (as generated by 4-sided dice)Can you predict if 100 numbers in pattern 2 are given ??

Randomization decreases Predictability Increases Security

Region 1 Region 2

Region 3 Region 4


Problem Definition

Problem : Increase security by decreasing predictability for agent-team acting in adversarial environments. Even if Policy Given, it is Secure Environment is stochastic and observable (MDP-based) Communication is a limited Efficient Algorithms for

Reward/Randomization/Communication Tradeoff


Assumptions

Assumptions for agent-team: Adversary is unobservable

– Adversary’s actions/capabilities or payoffs are unknown Communication is encrypted (safe)

Assumptions for Adversary: Knows the agents plan/policy Exploits action predictability Can see the agent’s state


Solution Technique

Technique developed: Intentional policy randomization CMDP based framework :

– Sequential Decision Making

– Limited Communication Resources

– CMDP Constrained Markov Decision Process

Increase Security => Solve Multi-criteria problem for agents Maximize action unpredictability (Policy randomization) Maintain reward above threshold (Quality constraints) Communication usage below threshold (Resource constraints)


Domains

Scheduled activities at airports like security check, refueling etc Can be observed by adversaries Randomization of schedules helpful

UAV-team patrolling humanitarian mission Adversary disrupts mission – Can disrupt food, harm refugees,

shoot down UAV’s etc Randomize UAV patrol policy


Our Contributions

1. Randomized policies for Multi-agent CMDP (MCMDP)

2. Solve Miscoordination Randomized polices in team settings

– Policy not implementable!

(Reward constraint gets violated)

Communication Resource <Threshold

Expected TeamReward >Threshold

Maximize Policy

Randomization


Miscoordination: Effect of Randomization

Meeting tomorrow 9am – 40%, 10am – 60%

Communicate to coordinate Limited Communication

Agent 1/ Agent 2

9 am

(.4)

10 am

(.6)

9am (.4) .16 .24

10am (.6) .24 .36

Should have been 0(Violates Threshold

Rewards)


Communication Issue

Generate Randomized Implementable policies Limited communication

Problem of communication M coordination points N units of communication Generate best communication policy Communication policy can also be randomized

Transform MCMDP to implementable MCMDPSolution algorithm for transformed MCMDP


MCMDP: Formally Defined

An MCMDP (for a 2 agent case) is a tuple

<S,A,P,R, C1,C2, T1,T2, N,Q> where, S,A,R – Joint states, actions, rewards P – Transition function C1 - Cost vector for resource k T1 - Threshold on expected resource k consumption. N - Joint communication cost vector Q - Threshold on communication costs

Basic terms used : x(s,a) : Expected times action a is taken in state s Policy (as function of x) :

^

^

( , ) ( , ) / ( , )a A

s a x s a x s a


Entropy : Measure of randomness

Randomness or information content quantified using Entropy ( Shannon 1948 )Entropy for CMDP - Additive Entropy – Add entropies of each state

Weighted Entropy – Weigh each state by it contribution to total flow

where alpha_j is the initial flow of the system

H x s a s aAs S a A

( ) ( ( , ) lo g ( , ))

H x

x s a

s a s aWa A

jj S

a As S

( )

( , )

( , ) lo g( ( , ) )

^

^


Issue 1: Randomized Policy Generation

Non-linear Program: Max entropy, Reward above threshold, Communication below threshold

Obtains required randomization

Appends communication for every action

Issue 2: Generate the Communication Policy

QNx

RRx

x

alphaAxst

xH w

min

0

)(max


Issue 2: Transformed MCMDP

11ba

12ba

22ba

S1S1

a2o

a2C

a1o

a1C

For each state, for each joint action,

Transition between original and new statesTransitions between new states and original target states

Introduce C (communication) and NC for different individual action, add corresponding new states

21ba )( 1aC

)( 1aNC)( 2aC

)( 2aNC

a1b1a1b2

a1b1a1b2

a2b1a2b2

a2b1a2b2


Non-linear Constraints

Need to introduce non-linear constraints

For each original state For each new state introduced by no communication action

– Conditional probability of corresponding actions equal

Ex: P(b1/ ) = P(b1/ ) &&

P(b2/ ) = P(b2/ )

, - Observable, Reached by Comm action

, - Unobservable, No Comm action

A o1 A o2

A o1 A o2

A c1 A c2

A o1 A o2


Non-Linear constraints: Handling Miscoordination

Agent B has no hint of state if NC actions. Necessity to make its actions independent of source state. Probability of action b1 from state should equal

probability of same action (i.e b1) from .

Meeting scenario: Irrespective of agent A’s plan If agent B’s plan is 20% 9am & 80% 10am B is independent of A

Miscoordination avoided Actions independent of state.

A o1A o2


Experimental Results

0 1 2 3 4 5 6

> 11> 7

> 3

0

0.5

1

1.5

2

Weighted Entropy

Communication Threshold

Reward (>1 to >11)

Entropy vs Reward vs Communication

X-axis

Y –

axis

Z-axis


Experimental Conclusions

Reward Threshold decreases => Entropy increases

Communication increases => Agents coordinate better Coordination invisible to adversary Agents coordinate better to fool the adversary

Increased communication Higher entropy !!!


Summary

Randomized Policies in Multiagent MDP settings

Developed NLP to maximize weighted entropy with reward and communication constraints.

Provided transformation algorithm to explicitly reason about communication actions.

Showed that communication increases security.


Thank You

Any Questions ???

Increasing Security through Communication and Policy Randomization in Multiagent Systems

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