Gossip-Based Aggregation of Trust in Decentralized Reputation Systems

Gossip-Based Aggregation of Trust in Decentralized Reputation SystemsAriel D. Procaccia, Yoram Bachrach, and Jeffrey S. RosenscheinAriel D. Procaccia, Yoram Bachrach, and Jeffrey S. Rosenschein

Lecture OutlineLecture Outline

IntroductionGossip-based algorithmsOur approachFeatures

Motivates truthfulnessImpervious to attacks

Conclusions

IntroductionGossip-based algorithmsOur approachFeatures

Motivates truthfulnessImpervious to attacks

Conclusions

Introduction Gossip-Based Our Approach Features Conclusions

BackgroundBackground

Multiagent environments are often teeming with self-interested agents which are continually interacting.

Agents may be tempted to employ deceit, but dishonest agents can expect their victims to retaliate.

This motivates cooperation and trustworthiness.

Multiagent environments are often teeming with self-interested agents which are continually interacting.

Agents may be tempted to employ deceit, but dishonest agents can expect their victims to retaliate.

This motivates cooperation and trustworthiness.

Introduction Gossip-Based Our Approach Features Conclusions

Reputation SystemsReputation Systems

As number of agents grows, agents have smaller chance to interact with agents they know.

Building trust becomes harder. Reputation systems collect and

spread reports among agents. Agents learn from others’

experience.

As number of agents grows, agents have smaller chance to interact with agents they know.

Building trust becomes harder. Reputation systems collect and

spread reports among agents. Agents learn from others’

experience.

Introduction Gossip-Based Our Approach Features Conclusions

MotivationMotivation

Reputation systems decompose into:Trust model. Data management scheme.

Data management solutions:Central database: inappropriate. Previous suggestions plagued by:

large data structures, evaluation of trust is based on local information.

Reputation systems decompose into:Trust model. Data management scheme.

Data management solutions:Central database: inappropriate. Previous suggestions plagued by:

large data structures, evaluation of trust is based on local information.

Introduction Gossip-Based Our Approach Features Conclusions

The Telephone Call Problem

The Telephone Call Problem

Introduction Gossip-Based Our Approach Features Conclusions

Computing Aggregate InfoComputing Aggregate Info

Push-Sum [Kempe et al. 2003] computes avg of values at nodes.

At each turn, each node maintains sum and weight. Sends half of sum and weight to node chosen randomly. Current evaluation: sum/weight.

The diffusion speed of uniform gossip U(n,,) is an upper bound on the number of turns required so that the error at each node is at most with probability 1-.

Push-Sum [Kempe et al. 2003] computes avg of values at nodes.

At each turn, each node maintains sum and weight. Sends half of sum and weight to node chosen randomly. Current evaluation: sum/weight.

The diffusion speed of uniform gossip U(n,,) is an upper bound on the number of turns required so that the error at each node is at most with probability 1-.

Introduction Gossip-Based Our Approach Features Conclusions

Computing Aggregate InfoComputing Aggregate Info

Theorem: U(n,,)=O( logn + log(1/)+log(1/)).

Aggregation persists in face of failures.

Still works when point-2-point communication cannot be assumed, e.g. in peer-2-peer networks.

Theorem: U(n,,)=O( logn + log(1/)+log(1/)).

Aggregation persists in face of failures.

Still works when point-2-point communication cannot be assumed, e.g. in peer-2-peer networks.

Introduction Gossip-Based Our Approach Features Conclusions

r21NA

r221

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A demonstrationA demonstration

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r11NA

r121

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r111

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r221

r230.9

r24NA

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r331

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r320.6

r331

r34NA

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r13NA

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Introduction Gossip-Based Our Approach Features Conclusions

Should I deal with 2?

Details of approachDetails of approach

Each agent i maintains evaluation rij of

agents j it interacted with. Let rj=krk

j. When interacting with j, i obtains rj using Push-Sum. Inputs are rk

j. Salient features:

Decentralization. Scalability. Robustness to failure. Globality. Simple data structures.

Each agent i maintains evaluation rij of

agents j it interacted with. Let rj=krk

j. When interacting with j, i obtains rj using Push-Sum. Inputs are rk

j. Salient features:

Decentralization. Scalability. Robustness to failure. Globality. Simple data structures.

Introduction Gossip-Based Our Approach Features Conclusions

Motivates TruthfulnessMotivates Truthfulness

A priori, makes sense to be dishonest on occasion.

Each agent has thresholds rithr, i.

Must repeatedly decrease until sure of result.

Theorem: Let ij=|rj-rithr|. Then the

time to decide is O( logn + log(1/i) + log(1/ij)).

Higher reputation close deals faster.

A priori, makes sense to be dishonest on occasion.

Each agent has thresholds rithr, i.

Must repeatedly decrease until sure of result.

Theorem: Let ij=|rj-rithr|. Then the

time to decide is O( logn + log(1/i) + log(1/ij)).

Higher reputation close deals faster.

Introduction Gossip-Based Our Approach Features Conclusions

Impervious to attacksImpervious to attacks

During Push-Sum, agents repeatedly update evaluation.

Consider: i maintains sum/weight=1. Theorem: at each node, evaluation of

average converges to 1 in probability. Theorem: after T stages, the

expected difference in the average T/2n.

Insubstantial when T=O(logn).

During Push-Sum, agents repeatedly update evaluation.

Consider: i maintains sum/weight=1. Theorem: at each node, evaluation of

average converges to 1 in probability. Theorem: after T stages, the

expected difference in the average T/2n.

Insubstantial when T=O(logn).

Introduction Gossip-Based Our Approach Features Conclusions

Proof SketchProof Sketch

w S

wSS

w

wS

w Sw

S

w

w

S

S+

Introduction Gossip-Based Our Approach Features Conclusions

Proof SketchProof Sketch

The difference in total sum, in stage t, is at most the total weight sent to the manipulator.

The expected weight sent to the manipulator at stage t is ½.

Linearity of expectation multiply by T.

Divide by n to obtain difference in average.

The difference in total sum, in stage t, is at most the total weight sent to the manipulator.

The expected weight sent to the manipulator at stage t is ½.

Linearity of expectation multiply by T.

Divide by n to obtain difference in average.

Introduction Gossip-Based Our Approach Features Conclusions

ConclusionsConclusions

Features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. Motivates Truthfulness. Impervious to certain attacks.

Some existing trust models are compatible [Aberer and Despotovic 2001, Xiong and Liu 2003].

Features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. Motivates Truthfulness. Impervious to certain attacks.

Some existing trust models are compatible [Aberer and Despotovic 2001, Xiong and Liu 2003].

Introduction Gossip-Based Our Approach Features Conclusions