A Distributed, Complete Method for MultiAgent Constraint Optimization

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A Distributed, Complete Method forMulti-Agent
Constraint Optimization

• Adrian Petcu, Boi Faltingsadrian.petcu_at_epfl.ch
  boi.faltings_at_epfl.ch Artificial Intelligence
  LaboratorySwiss Federal Institute of Technology
  (EPFL)IN-Ecublens, 1015 Lausanne,
  Switzerlandhttp//liawww.epfl.ch/People/apetcu/

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Overview

• Problem description
• DTREE tree propagation algorithm
• CyPro utility propagation with cycles
• CyCopt splitting the problem
• Conclusions future work

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Multi-agent Constraint Optimization (MCOP)

• Constraint Optimization Problems (COP) tuple
  ltX, D, Rgt
• MCOP multi-agent version of COP in general,
  one variable per agent
• MCOP solutions have a quality to be maximized
  (constraints are utility functions, not
  predicates)

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Overview

• Problem description
• DTREE tree propagation algorithm
• CyPro utility propagation with cycles
• CyCopt splitting the problem
• Conclusions future work

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DTREE (1) main ideas

• Distributed utility propagation algorithm
• The leaves of the tree initiate the propagation,
  and then all nodes forward messages by the k-1
  rule
• Nodes terminate after receiving all k messages (k
  neighbors, one message each)
• 2 x (n-1) fixed size messages transmitted.

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DTREE (2) message dynamics
x0
x4
x1
x3
x6
x7
x5
x2
Done!
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DTREE (3) computation details
X2?X1
X1?X0
X3?X1
R(X1,X0)
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Overview

• Problem description
• DTREE tree propagation algorithm
• CyPro utility propagation with cycles
• CyCopt splitting the problem
• Conclusions future work

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CyPro(1)

• Idea reduce a complex problem (with cycles) to
  separate cycle-free parts
• Choose a set of cycle cut nodes, and initiate
  propagation from them.
• Explore all combinations of values of CC nodes,
  and have them assemble the results

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CyPro(2)
normal nodes forward by the k-1 rule, and
combine contexts
Xj,Xk
Xj,Xk
Xkvk0
Xjvj0
Tree parts send messages as before
Cycle cuts act like leaves
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Overview

• Problem description
• DTREE tree propagation algorithm
• CyPro utility propagation with cycles
• CyCopt splitting the problem
• Conclusions future work

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CyCOpt(1)

• Cyclic sub graphs can be processed independently
  if they are connected through only one CC node.
• A meta-tree is formed by CC nodes and cyclic sub
  graphs
• Processing in the meta-tree proceeds like in DTREE

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CyCOpt(2)
Xj
Xk
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Overview

• Problem description
• DTREE tree propagation algorithm
• CyPro utility propagation with cycles
• CyCopt splitting the problem
• Conclusions future work

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Conclusions future work

• Linear message size, linear memory
• Reduction in complexity from domn gtgt domCCgtgt
  domCCs in largest subgraph
• Choice of the cycle cutset is important
• Exhaustive search within a cyclic subgraph is
  maybe not necessary

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References

• F. Kschischang, B.Frey, and H. Loeliger. Factor
  graphs and the sum-product algorithm. IEEE
  TRANSACTIONS ON INFORMATION THEORY, 2001.
• Rina Dechter. Constraint Processing. Morgan
  Kaufmann, 2003.
• P. Modi, W. Shen, M. Tambe, and M. Yokoo. An
  asynchronous complete method for distributed
  constraint optimization, 2003.