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Towards a Formal Framework for Hybrid Planning in Self-Adaptation

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A presentation from SEAMS 2017 on formalization of hybrid planning.
Lead author: https://www.cs.cmu.edu/~ashutosp/
Full paper: http://www.cs.cmu.edu/~iruchkin/docs/pandey17-towards.pdf

Abstract: "Decision-making approaches in self-adaptation face a fundamental trade-off between quality and timeliness of adaptation plans. Due to this trade-off, designers often have to make an offline compromise between finding adaptation plans quickly and finding closer-to-optimal plans that demand longer computation times. Recent work has proposed that hybrid planning can resolve this trade-off dynamically, achieving higher utility than either fast or slow approaches individually. The promise of hybrid planning is to combine multiple decision-making approaches at run time to produce adaptation plans of the high quality within given time constraints. However, the diversity of decision-making approaches makes the problem of hybrid planning complex and multi-faceted. This paper advances the theory of hybrid planning by formalizing the central concepts and four sub-problems of hybrid planning. This formalization can serve as a foundation for creating and evaluating hybrid planners in the future."

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Towards a Formal Framework for Hybrid Planning in Self-Adaptation

  1. 1. TOWARDS A FORMAL FRAMEWORK FOR HYBRID PLANNING IN SELF-ADAPTATION Ashutosh Pandey Ivan Ruchkin Bradley Schmerl Javier Cámara SEAMS 2017 (The 12th International Symposium on Software Engineering for Adaptive and Self-Managing Systems)Buenos Aires, Argentina · 22-23 May 2017 1
  2. 2. KEY REQUIREMENTS: QUALITY AND TIMELINESS OF DECISION-MAKING ➤ Although these systems are designed for balancing multiple objectives to provide long term quality ➤ Amazon web services primarily cares about availability1 ➤ Netflix primarily cares about response-time perceived by clients2 1.https://aws.amazon.com/ec2/sla/ 2.http://techblog.netflix.com/2010/12/5-lessons-weve-learned-using- aws.html 2
  3. 3. CONFLICTING REQUIREMENTS: QUALITY AND TIMELINESS OF DECISION-MAKING Desired Region Probabilistic Planning Ex: MDP, POMDP Case-based Reasoning Ex: Rainbow framework Heuristic Planning Ex: FF-Replan Reactive Planning Ex: Condition-action rules Decision-making Time DecisionQuality 3 *WOLPERT, David H., and William G. MACREADY, 1995. No free lunch theorems for search. Technical Report SFI-TR-95-02-010. Sante Fe, NM, USA: *WOLPERT, David H., and William G. MACREADY, 1997. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67–82.
  4. 4. HYBRID PLANNING 4 𝛒 Fast 𝛒 slow 𝛱Fast t 𝛱Slow t’ Planning Process 𝛒 ➜ Planner 𝛱 ➜ Plan Timeline Planning Problem
  5. 5. Slow Planner ⇒ Planner based on Markov Decision Processes (MDP) Fast Planner ⇒ Deterministic planner HYBRID PLANNING LOOKS PROMISING!! 5 0 1 0.5 -0.5 -1.0 -1.5 1.5 Fast Planner Slow Planner Hybrid Planner Normalized Aggregate Utility A. Pandey et. al. Hybrid planning for decision making in self- adaptive systems. International Conference on Self-Adaptive and Self-Organizing Systems, SASO 2016, pp. 12-16
  6. 6. THE PROBLEM OF HYBRID PLANNING 6
  7. 7. THE PROBLEM OF HYBRID PLANNING “Given a planning problem, and a set of planners, find a hybrid plan that maximizes a posteriori utility.” 7
  8. 8. THE PROBLEM OF HYBRID PLANNING “Given a planning problem, and a set of planners, find a hybrid plan that maximizes a posteriori utility.” 8
  9. 9. “Given a planning problem, and a set of planners, find a hybrid plan that maximizes the a posteriori utility.” A PLANNING PROBLEM 9 S, si, A, o, T, Ue Set of states Initial state Transition function T : S x A x Z → S Environment o : S → Z A posteriori utility function Set of controllable actions Set of uncontrollable actions
  10. 10. A POSTERIORI UTILITY 10 High Load Add-Server H igh-Load Low Load Medium Load Low -Load Add-Server Low-Load High-Load Add-Server = High Load Medium Load High Load Low Load U U’ A Priori A Posteriori
  11. 11. 11 THE PROBLEM OF HYBRID PLANNING “Given a planning problem, and a set of planners, find a hybrid plan that maximizes a posteriori utility.”
  12. 12. 12 REACHABILITY GRAPH Pb U1 E1 Pb2 Pl2 Pb Pl1 Pb Planning problem Pl Planner E Execution U A posteriori utility d Deadline to trigger a planner Problem-Planner node Execution edge
  13. 13. 13 REACHABILITY GRAPH Pb Pl1Pb U1 E1 Pb2 Pl2 E1 U1 Pb2 Pl3 Pb Planning problem Pl Planner E Execution U A posteriori utility d Deadline to trigger a planner Problem-Planner node Execution edge
  14. 14. 14 REACHABILITY GRAPH Pb Pl1Pb U1 E1 Pb2 Pl2 E1 U1 Pb2 Pl3 E2 U2 Pb3 Pl4 E2 U2 Pb3 Pl5 Pb Planning problem Pl Planner E Execution U A posteriori utility d Deadline to trigger a planner Problem-Planner node Execution edge
  15. 15. 15 REACHABILITY GRAPH Pb Pl1Pb U1 E1 Pb2 Pl2 E1 U1 Pb2 Pl3 E2 U2 Pb3 Pl4 E2 U2 Pb3 Pl5 E3 U3 En Un Pbi Plj Pb Planning problem Pl Planner E Execution U A posteriori utility d Deadline to trigger a planner Problem-Planner node Execution edge
  16. 16. 16 REACHABILITY GRAPH Pb Pl1Pb U1 E1 Pb2 Pl2 E1 U1 Pb2 Pl3 E2 U2 Pb3 Pl4 E2 U2 Pb3 Pl5 E3 U3 En Un Pbi Plj Pb Planning problem Pl Planner E Execution U A posteriori utility d Deadline to trigger a planner Problem-Planner node Execution edge
  17. 17. 17 REACHABILITY GRAPH WHEN PLANNING TIME IS NOT ZERO Pb Pl1 dl1 Pb U1 E1 Pb2 Pl2 dl2 E1 U1 Pb2 Pl3 dl3 E2 U2 Pb3 Pl4 dl4E2 U2 Pb3 Pl5 dl5 E3 U3 En Un Pbi Plj dlk Pb Planning problem Pl Planner E Execution U A posteriori utility dl Deadline to trigger a planner Problem-Planner node Execution edge
  18. 18. 18 SOLVING THE HYBRID PLANNING PROBLEM Pb Pl1 dl1 Pb U1 E1 Pb2 Pl2 dl2 E1 U1 Pb2 Pl3 dl3 E2 U2 Pb3 Pl4 dl4E2 U2 Pb3 Pl5 dl5 E3 U3 En Un Pbi Plj dlk Pb Planning problem Pl Planner E Execution U A posteriori utility dl Deadline to trigger a planner Problem-Planner node Execution edge
  19. 19. 19 DECOMPOSITION OF THE PROBLEM OF HYBRID PLANNING Assessment of planners w.r.t.to problems Set of planning problems Planning problem Sequence of nodes from the reachability graph Reachability Graph Set of planning problems Set of planners and Problem-Planner Compatibility Relationship GPHCON PTHSELPRBSEL PLRAST
  20. 20. 20 SUB-PROBLEM: THE PATH SELECTION (PTHSEL) Assessment of planners w.r.t.to problems Set of planning problems Planning problem Sequence of nodes from the reachability graph Reachability Graph Set of planning problems Set of planners and Problem-Planner Compatibility Relationship GPHCON PTHSELPRBSEL PLRAST
  21. 21. 21 SUB-PROBLEM: THE GRAPH CONSTRUCTION (GPHCON) Assessment of planners w.r.t.to problems Set of planning problems Planning problem Sequence of nodes from the reachability graph Reachability Graph Set of planning problems Set of planners and Problem-Planner Compatibility Relationship GPHCON PTHSELPRBSEL PLRAST
  22. 22. 22 SUB-PROBLEM: THE PLANNER ASSESSMENT (PLRAST) Assessment of planners w.r.t.to problems Set of planning problems Planning problem Sequence of nodes from the reachability graph Reachability Graph Set of planning problems Set of planners and Problem-Planner Compatibility Relationship GPHCON PTHSELPRBSEL PLRAST
  23. 23. 23 SUB-PROBLEM: THE PLANNING-PROBLEM SELECTION (PRBSEL) Assessment of planners w.r.t.to problems Set of planning problems Planning problem Sequence of nodes from the reachability graph Reachability Graph Set of planning problems Set of planners and Problem-Planner Compatibility Relationship GPHCON PTHSELPRBSEL PLRAST
  24. 24. 24 ASSUMPTIONS FOR THE FORMAL FRAMEWORK ➤ No instantaneous actions ➤ Markovian domain ➤ Instantaneous solution to sub-problems ➤ Known worst-case planning time ➤ Known utility of executions
  25. 25. CONCLUSION ➤ Hybrid Planning approach is useful but a non-trivial problem to solve ➤ This formalism could help in understanding and approximating a more general solution to the problem 25
  26. 26. ACKNOWLEDGEMENT •This work is supported in part by awards •N000141310401 and N000141310171 from the Office of Naval Research (ONR) •FA87501620042 from the Air Force Research Laboratory (AFRL) 26
  27. 27. 27

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