1. 1 Risk Based Negotiation of Service Agent Coalitions Bastian Blankenburg, Matthias KluschDFKI Minghua He, Nick JenningsUniversity of Southampton

2. 2 Service Provider Agents Independent Rational Collaboration of Service Agents spa 1 ws 1 spa 2 ws 2 spa 3 ws 3 sra 1 Service Requesters Plan: Deadline: t 1 Deadline: t 2

3. 3 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

4. 4 Planning and Coalition Formation How to integrate composition planning and coalition formation? Plan-driven negotiation –Generate plans first –Negotiate and implement coalitions –Dynamics: short-term small coalitions Coalition-based planning –Form promising coalitions –Generate plans within the coalitions –Dynamics: DCF-S to add/remove agents as necessary (Klusch/Gerber 2002) Mutually controlled negotiation and planning –Integrates plan-driven negotiation and coalition-based planning

5. 5 Integration of Composition Planning and Coalition Negotiation spa 1 ws 1 spa 2 ws 2 Plan-driven negotiation 1. Plan 2. Coalesce, execute, share profit spa 1 ws 1 spa 2 ws 2 spa 1 ws 1 spa 2 ws 2 3. Separate

6. 6 Example: Medical Information Provision Request diagnosis, offer: 250€, deadline: 10min spa 1 spa 2 spa 3 Coalition Proposal C 1 reward: 250€ my costs: 10€ deadline: 10min my runtime: 5-6min Coalition Proposal C 2 reward : 150€ my costs: 15€ deadline: 10min my runtime: 1-2min C 1 my runtime: 3-5min my costs: 40€ Might fail! C 2 my runtime: 1-2min my costs: 10€ On the safe side! If C 2 then I can afford to risk C 1 ! ws 1 ws 2 ws 3

7. 7 Provider Agent Coalitions DB spa 1 DB spa 2 DB spa 3 Coalition Proposal C 1 reward: 250€, deadline: 9min Coalition Proposal C 2 reward : 150€, deadline: 5min spa 2 needs e.g. ca.5-6 min for C 1, 3-4 min for C 2 Form concurrent coalitions Reduce overall risk by dividing resources. How to divide the payoff? How to find good subset of coalitions in the general case? ?

8. 8 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

9. 9 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 Composition Plan: spa 1 spa 2

10. 10 Fuzzy 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

11. 11Example

12. 12 Stability in SPA Fuzzy Coalitions 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!

13. 13 Stability in SPA Fuzzy 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

14. 14 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

15. 15Complexity 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

16. 16 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

17. 17 RFCF Approach Exponential How to make it polynomial –drawbacks

18. 18 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

19. 19 Example (3)

20. 20Conclusions 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?