Risk Based Negotiation of
Service Agent Coalitions
Bastian Blankenburg, Matthias Klusch
Minghua He, Nick Jennings
DFKI
University of Southampton
1
Collaboration of Service Agents
Service Requesters
Service Provider Agents
• Independent
• Rational
sra1
spa1
ws1
spa2
ws2
Deadline: t1
Plan: <ws2,ws1>
spa3
ws3
Deadline: t2
Plan: <ws3,ws1,ws2>
2
Service Agent Coalition Formation
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
3
Example: Medical Information Provision
Request diagnosis, spa1
offer: 250€,
ws1
deadline: 10min
Coalition Proposal C1
reward:
250€
my costs: 10€
deadline: 10min
my runtime: 5-6min
spa2
ws2
spa3
ws3
Coalition Proposal C2
reward :
150€
my costs: 15€
deadline: 10min
my runtime: 1-2min
C1
my runtime: 3-5min
my costs: 40€
Might fail!
C2
my runtime: 1-2min
my costs: 10€
On the safe side!
If C2 then I can
afford to risk C1!
6
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
risk ( X  Y )  risk ( X )  risk (Y )
– Tail Conditional Expectation TCE
TCE   E  X | X  inf x   : P X  x    
• Expected loss in α worst cases
• Based on Value-at-Risk
8
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
spa2
spa1
Composition Plan:
0,25
0,45
0,4
0,2
0,35
0,3
0,15
0,25
0,2
0,1
0,15
0,1
0,05
0,05
0
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
0
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

pdf tPlan( x)   pdf tA ( y ) pdf tB ( x  y )dy
0
 F 1 ( F ( pdf tA ) F ( pdf tB ))

PoF ( Plan, tStart, DL ) 
 pdf
tPlan
( x)dx
DL tStart
PoS  1  PoF
9
Fuzzy Coalition Model
~
C
~
C  ({spa1 / mem1;; span / memn }, sra, Plan)
• 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
~
r  PoS (C )  r
~
C
v(C )  r C~ 
 cost
i
instances
• Fuzzy coalition structure
– Set of fuzzy coalitions
– Feasibility wrt. resources
spa :  mem
~
CS
~
C
spa
1
10
Stability in SPA Fuzzy Coalitions
Membership vs. PoS
• Existing approaches (Aubin;
Bunariu;Nishizaki,Sakawa)
Mean Runtime
PoS = P (Runtime < 4)
PoS = P (Runtime < 7)
80
1,0
0,9
70
0,8
60
0,7
Minutes
• 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!
Single-agent coalition, normal distribution with min. mean
runtime = 3, σ=1/mem.
50
0,6
40
0,5
0,4
30
0,3
20
0,2
10
0,1
0
0,0
100%
0%
20%
40%
60%
80%
Membership
12
Stability in SPA Fuzzy Coalitions (2)
e(C, u)  v(C ) 
• 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

aC
u (a)
• 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
~
~
~
e(C , u)  v|TCE (C )  aC~ min. payoff attenuatio n|TCE (a, C )
13
Stability in SPA Fuzzy 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
14
Complexity
• 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
15
Rational 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
16
RFCF Outline
Each agent performs in parallel:
•
Composition Planning
•
Coalition Negotiation
1. Proposal generation
i. Minimize memberships s.t. risk is acceptable
ii. Maximize payoff / membership
2. Proposal evaluation: form feasible coalitions with
i. acceptable risk
ii. maximal payoff / membership
3. Payoff distribution and risk bound update
i. Transfer Scheme
ii. Compute single-coalition TCE and add to coalition structure TCE
•
Risk Measure Computation
1. Compute exact TCE for new random subset of coalitions
until service execution start time
18
Conclusions
• 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?
20