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Planing under multiple consumable resources constraints

Planing under multiple consumable resources constraints. Simon Le Gloannec MAIA team (Nancy) MAD team (Caen). Outline. The problem description Tools & Techniques Approach Results Improvements & future works Perspectives. Problem description. Planing (single autonomous agent).

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Planing under multiple consumable resources constraints

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  1. Planing under multiple consumable resources constraints Simon Le Gloannec MAIA team (Nancy) MAD team (Caen)

  2. Outline • The problem description • Tools & Techniques • Approach • Results • Improvements & future works • Perspectives

  3. Problem description • Planing (single autonomous agent). • Real time. • Real environment. • Multiple bounded resources : energy, time. • Dynamic Task selection. • Add or remove tasks dynamically.

  4. Tools & Techniques • Progressive processing [Moua, Zilb 98] Task Task Select Task new Task Task Continue and Improve

  5. My approach • MDP : • States : resources left × current task • Action : Continue , Select • Transition : model known in advance • Reward : Given by an expert

  6. My approach Opportunity cost [Zilb, Moua, Arnt 00] • Should it spent more ressources in the current task ? • Should it keep ressources for the remaining tasks ? OC( R) = VE( R) – VE ( 0)

  7. Approximation Opportunity cost • We can calculate the OC to find the optimal policy. (global policy) Not at run time. • Make an approximation of OC. Decompose the MDP

  8. decomposition • Decomposition + recomposition • An MDP for each task VE( R) R Task REstimated ( R) Data base E

  9. VE e REstimated VE is increasing in R t Multi resources • Multi resources : R = [e, t] (energy, time) • Huge state space Lots of states with the same value

  10. Compact representation 5 0 2 2 3 7 10 4 0 2 2 3 7 10 3 0 2 2 3 7 7 2 0 2 2 3 4 4 1 0 1 2 2 2 2 0 0 0 0 0 0 0 0 1 2 3 4 5 R2 = energy R1 = time

  11. OC( R) = VE( R) + (VE ( R) +(VE ( R) )) R = R - REstimated Recomposition • Recomposition (Approximate OC) • Allocate R in the different tasks • Sort Task by VE Task Task Task + + Data base

  12. Results • Error measure • Queue depth • All possible starting resources • Decision Error • Continue or move ?

  13. Improvements & future works • Make a first approximation of OC( R) and refine the solution with an anytime algorithm • Bound the error (mathematically) • Find a contraction

  14. Bibliography • [Moua, Zilb 98] Optimal Scheduling for Dynamic Progressive Processing, ECAI 98 • [Zilb, Moua, Arnt 00] Dynamic composition of problem solving techniques, ECAI 2000

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