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Risk Based Negotiation of Risk Based Negotiation of

Service Agent CoalitionsService Agent Coalitions

Bastian Blankenburg, Matthias Klusch DFKIMinghua He, Nick Jennings University of Southampton

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Service Provider Agents• Independent• Rational

Collaboration of Service AgentsCollaboration of Service Agents

spa1

ws1

spa2

ws2

spa3

ws3

sra1

Service Requesters

Plan: <ws2,ws1>

Plan: <ws3,ws1,ws2>

Deadline: t1

Deadline: t2

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Service Agent Coalition Service Agent Coalition FormationFormation

Coalition negotiation• Set of requests, set of composition plans• Which plans to execute?

– Do the agents have enough resources?– Is a plan profitable?– What about the costs in case of failure?

• How to share the profit (or loss)?– Stability: avoid that agents break their

coalitions

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Example: Medical Information Example: Medical Information ProvisionProvision

Request diagnosis,offer: 250€,

deadline: 10min

spa1

spa2

spa3

Coalition Proposal C1

reward: 250€ my costs: 10€deadline: 10minmy runtime: 5-6min

Coalition Proposal C2

reward : 150€my costs: 15€ deadline: 10minmy runtime: 1-2min

C1

my runtime: 3-5min

my costs: 40€Might fail!

C2 my runtime: 1-

2minmy costs: 10€On the safe

side!If C2 then I can afford to risk

C1!

ws1

ws2

ws3

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Assessing Coalition Risk (1)Assessing Coalition Risk (1)

Financial Risk Measures

• Informal Definition– Combination of the probability of undesirable

outcomes and their net results

• Coherency (Artzner et al. 1999)– Translation invariance, positive homogenity,

monotonicity, subadditivity

– Tail Conditional Expectation TCE

• Expected loss in α worst cases• Based on Value-at-Risk

)()()( YriskXriskYXrisk

xXPxXXETCE :inf|

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Assessing Coalition Risk (2)Assessing Coalition Risk (2)

• Service instances in a plan are executed sequentially

• Probability functions for instance runtimes

• Composed service runtime

– Sum of random variables: convolution of PDFs

– Equal to point-wise multiplication of Fourier Transforms

– Fast approximation with FFT

• Probability of Failure/Success

))()((

)()()(

1

0

tBtA

tBtAtPlan

pdfFpdfFF

dyyxpdfypdfxpdf

PoFPoS

dxxpdfDLtStartPlanPoFtStartDL

tPlan

1

)(),,(

Composition Plan:

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 6,50

0

0,05

0,1

0,15

0,2

0,25

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 6,50 7,00 7,50 8,00 8,50 9,00 9,50 10,00

spa1

spa2

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Fuzzy Coalition ModelFuzzy Coalition Model

• Fuzzy Coalition– Bound to request and plan– Coalition membership degree in

[0,1]– Fraction of resources per time– Determines service instance

runtimes, PoF and PoS

• Values of a fuzzy coalition– Reward r is paid only if of

successful– Expected reward– Expected value

• Fuzzy coalition structure– Set of fuzzy coalitions– Feasibility wrt. resources

instances

~

~

cost)(

)~

(

iC

C

rCv

rCPoSr

C~

),},/;;/({~

11 PlansramemspamemspaC nn

SC

~

C~

1mem: spaspa

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Membership vs. PoSSingle-agent coalition, normal distribution with min. mean

runtime = 3, σ=1/mem.

0

10

20

30

40

50

60

70

80

0% 20% 40% 60% 80% 100%

Membership

Min

ute

s

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Mean Runtime PoS = P (Runtime < 4) PoS = P (Runtime < 7)

Stability in SPA Fuzzy Stability in SPA Fuzzy CoalitionsCoalitions

• Existing approaches (Aubin; Bunariu;Nishizaki,Sakawa)

• Shapley value, Core, Nucleolus and others

• Assumption: coalition value is proportional to membership degrees– does not hold– runtime is 1/x. – PoS/PoF and expected

value not proportional– PoS must not be

overestimated!

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Stability in SPA Fuzzy Stability in SPA Fuzzy Coalitions (2)Coalitions (2)

• Recall: excess of a coalition:• Excess of a fuzzy coalition

– Any amount of membership can be transferred– Coalition structure might be too risky for a member

• Should such coalitions be considered a feasible threat?• Mutual dependency of risk and payoff

– How is an agent‘s payoff affected by withdrawing a certain amount of membership?

– Consider conditional expected values

CaauCvuCe )()(),(

CaTCE CaCvuCe ~|TCE| )

~,(nattenuatio payoff min.)

~(),

~(

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Stability in SPA Fuzzy Stability in SPA Fuzzy Coalitions (3)Coalitions (3)

• Kernel – Surplus

• „I can gain more without you, than you without me“.• max. excess of coalitions excluding the other agent• With fuzzy coalitions, it is possible to transfer

membership to multiple other coalitions at the same time

– Kernel-stable solution: equilibrium of surplusses

– Computation: transfer scheme

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ComplexityComplexity

• Computation of surplus depends on computation

of TCE and vice versa• Both have exponential computation time • How to do it (highly) polynomial:

– Compute upper bounds for TCE:• Consider minimum individual rational payoffs• Use subadditivity when forming additional coalitions• Refine bounds while there is time

– Add some constraints to the game to compute surpluses

• Bound the max. coalition size, number of plans per coalition and number of coalitions that an agent can join

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Rational Service Agent ModelRational Service Agent Model

• Service Request Agent– Represents a SWS request– Specifies a deadline– Provides a monetary reward for timely execution

• Service Provider Agent– Offers one SWS– Has an SWS composition planning module– Has Bounded resources,– May split resources among multiple service instance

executions,– Computes probabilistic estimations of service instance

execution times, by e.g.• Learning • Stochastic process modeling (Manolache et al. 2004)

– Produces a fixed cost for any service execution

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RFCF OutlineRFCF Outline

Each agent performs in parallel:

• Composition Planning

• Coalition Negotiation1. Proposal generation

i. Minimize memberships s.t. risk is acceptableii. Maximize payoff / membership

2. Proposal evaluation: form feasible coalitions with i. acceptable riskii. maximal payoff / membership

3. Payoff distribution and risk bound updatei. Transfer Schemeii. Compute single-coalition TCE and add to coalition structure

TCE

• Risk Measure Computation1. Compute exact TCE for new random subset of coalitions

until service execution start time

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ConclusionsConclusions

• Adavantages– Anytime approach– Guaranteed risk bounds wrt. individual risk averseness– Gradually improvement of

• risk assessment• coalition structure

• Drawbacks/Simplifications – Complexity:

• Exact solution has exponential runtime• Constrained solution still has highly polynimial runtime

– Independent service runtime assumption– Static setting

• service execution start time• for the dynamic case: when to stop negotiation?