A Decision A Decision A Decision-Analytic Approach for A Decision - - PowerPoint PPT Presentation

A Decision A Decision Analytic Approach for Analytic Approach for A Decision A Decision-Analytic Approach for Analytic Approach for P2 2P Cooperation Policy Setting P Cooperation Policy Setting p y g p y g

G V k l 1 Th G P

2 S Kh

d 1 G. Vakili1, Th. G. Papaioannou2, S. Khorsandi1

1 Amirkabir University of Technology

Tehran Iran Tehran – Iran

2 Ecole Polytechnique Fédérale de Lausanne (EPFL)

Lausanne – Switzerland NetEcon’10

O tli O tli Outline Outline

Our Motivation & Goal Our Approach Our Approach System Model Decision-Analytic Approach Analysis Analysis

NE Analysis

Evaluation Conclusion

Conclusion

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O M ti ti & G l O M ti ti & G l Our Motivation & Goal Our Motivation & Goal

Overall performance of P2P systems depends on

resource contributions of individual peers.

Rational peers decide on their cooperation policies

according to their individual utilities according to their individual utilities.

Inherent conflict among individual utilities of the rational Inherent conflict among individual utilities of the rational

peers results in

free-riding unfair contribution low participation

Our goal is dealing with the inherent individual utility

conflicts to improve overall performance of the system conflicts to improve overall performance of the system.

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Our Approach Our Approach Our Approach Our Approach

We employ decision-theory to model cooperation

p y y p policy setting of participating peers:

Each peer chooses its strategy according to observable strategies of the other peers. Through a swarm-based iterative learning process:

R l h l Rational peers set their cooperation policies so as to maximize their own utility. Their decisions are coordinated in a distributed manner to Their decisions are coordinated in a distributed manner to improve the social welfare of the system.

The game-theoretic analysis lacks an explicit and

tractable handling of the individual strategy g gy dynamics present in the interactions among individual peers p

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SYSTEM MODEL SYSTEM MODEL SYSTEM MODEL SYSTEM MODEL

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Individual Individual-

• based Lagrangian

based Lagrangian Swarm Swarm Model Model

I t ti ti i t f P2P t hibit l

Interacting participants of a P2P system exhibit general

properties of an individual based Lagrangian swarm model: model:

composed of many individual peers; the interactions are based on local information exchange; g ; emergence; self-organization.

We made two modifications to adopt this model in

h f P2P the context of a P2P system:

Distributed local objectives (utility functions) are defined for individual peers individual peers. The interaction of particles is represented as a non- cooperative game.

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Definitions Definitions Definitions Definitions

We assume that N peers p ; i:1

N participate in

We assume that N peers pi ; i:1,…,N participate in

the system P li (d)

Policy (di)

a peer’s policy is its level of cooperation (a numerical t f th ’ t ib t d t th assessment of the peer’s contributed resources to the system)

St t ( )

Strategy (si)

the strategy of a peer reflects its decision on the change i it ti l l ( li ) in its cooperation level (policy)

Utility (Ui)

A peer's utility is determined by its strategy choices and depends on several parameters - discussed as follows.

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Utility Function Utility Function

Cost and Benefit

Utility Function Utility Function

the total cost for participating in the system with cooperation level of di will be cidi the benefit of cooperation of pj to pi is represented by bijdj ; where bij is measured (e.g.) as the inverse of latency

ij j ij

( g ) y

Incentives for high contribution Incentives for high contribution

it is modeled by a monotonically increasing function of h i li f d d b b the cooperation policy of a peer pi, denoted by bci

Utility:

; . . ≡ − =

∑

ii i i j ij i i

b d c d b bc U ;

∑

∈ ii i i N j j ij i i 8

DECISION DECISION-ANALYTIC ANALYTIC DECISION DECISION ANALYTIC ANALYTIC APPROACH APPROACH

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O ll O ll Overall Overall

Observable strategies of other peers are monitored by each peer in a sequence of iterations. p q Based on this empirical evidence each peer can decide Based on this empirical evidence, each peer can decide rationally on a strategy in every iteration. This chain of decisions are made based on a method i i d b ti l ti i ti (PSO) inspired by particle swarm optimization (PSO). Through this chain of decisions each participating peer concludes its final cooperation policy with respect to the

• ther peers' behavior.

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M F ll M F ll More Formally More Formally

T

• maximize its expected utility Ui , each peer pi sets its

final cooperation policy through an iterative decision k making process:

pi monitors the strategies of the other peers in its neighborhood N locally and evaluates their strategies Ni locally and evaluates their strategies. It chooses its strategy si

next in the next iteration with respect to

the evaluation result and to its own experience: d i h b i li f d d d h b li

) ( ) (

2 2 1 1 current i n current i p current i next i

d d c r d d c r s s − + − + =

dp is the best previous policy of pi and dn denotes the best policy

• f the other peers in Ni.

Then the cooperation policy di of peer pi is revised as follows:

next current next

s d d + =

i i i

s d d + =

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ANALYSIS ANALYSIS - ANALYSIS ANALYSIS EVALUATION EVALUATION

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NE A l i NE A l i NE Analysis NE Analysis

We employ Nash equilibrium analysis to investigate

the predicted strategies for the participating peers by th d i i l ti h the decision-analytic approach. A di [B

h i l P2PC i 03] f

According to [Buragohain et al. P2PComputing03] for a

similar quantitative model of the system in a homogeneous setting (for all pi bij = b ci= c) the NE is homogeneous setting (for all pi ,bij b, ci c), the NE is given by:

2 / 1 2

) 1 ) 1 2 / ) 1 ( (( ) 1 2 / ) 1 ( ( * ± N b N b d

As we numerically show:

2 / 1 2

) 1 ) 1 2 / ) 1 ( (( ) 1 2 / ) 1 ( ( * − − − ± − − = c N b c N b d

y

The expected NE of the game is not the Pareto-optimal one. The outcome derived from the proposed decision-analytic h ld k ll l b ff approach would make all players better-off.

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The comparison of the average The comparison of the average p g p g cooperation level cooperation level

7 8 9 evel 4 5 6 7

• peration L

1 2 3 4 Average Coo Hetero Homo NE 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A NE

Tendency toward Pareto efficiency

Scaled Benefit

Tendency toward Pareto efficiency

Better outcome than NE Both homogeneous and heterogeneous settings evolve

Both homogeneous and heterogeneous settings evolve similarly

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Convergence to a set of Pareto Convergence to a set of Pareto g efficient strategy efficient strategy

8 9 l 5 6 7 8 ation Leve 3 4 5 age Coopera Scaled Benefit = 0.05 1 2 Avera Scaled Benefit = 0.5 Scaled Benefit = 1 1 6 11 16 21 26 31 36 41 46 Number of Iterations

Fast convergence regardless of the target cooperation level

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CONCLUSION CONCLUSION CONCLUSION CONCLUSION

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C l i C l i F t W k F t W k Conclusion Conclusion – Future Work Future Work

We propose a decision-analytic approach based on the modified

swarm model, to set and coordinate rational decisions of the individual peers on their cooperation policies in a distributed individual peers on their cooperation policies in a distributed manner.

The resulting cooperation policies constitute the final set of

decisions that maximize rational peers' utility in-line with the social welfare of the system. y

Incentive-compatible for peers to follow

Our approach quickly approximates a Pareto-optimal operating

point of the system.

In our future work, we will investigate information exchange

mechanisms that involve incentives for neighbor truthfulness or

• wn observation and verification.

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THANK YOU FOR YOUR THANK YOU FOR YOUR ATTENTION. ATTENTION. MORE QUESTIONS TO: MORE QUESTIONS TO: Golnaz Vakili

g_vakili@aut.ac.ir Distributed Information Systems Lab, EPFL http://lsir.epfl.ch

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