Decentralised Coordination of Continuously Valued Control Parameters using the Max-Sum Algorithm

R. Stranders, A. Farinelli, A. Rogers, N. R. JenningsSchool of Electronics and Computer Science

University of Southampton, UK

References:

Empirical EvaluationFrom Discrete to Continuous

Contacts:

R. Stranders, A. Farinelli, A. Rogers, N. R. Jennings, School of Electronics and Computer ScienceUniversity of SouthamptonSouthampton, SO17 1BJ, UK.{rs06r,af2,acr,nrj}@ecs.soton.ac.uk

ApproachMax-Sum Algorithm used as starting point

Variable nodes Function nodes

Problem Formulation: global welfare maximisation through local computation:

Availability of devices acquiring and processing information from the environment.

Goal:Coordinate the activities of a set of devices characterised by continuously valued control parameters. For example:

• Part of the GDL framework• Graphical models,

Information theory• Message Content

• Functions of variable states • Message Propagation

• From Variable: aggregate information (Sum)

• From Functions: maximise sum of utility and variable messages (Max)

Optimal on trees, good approximation on cycle graphs

Motivation

• Stranders, R., Farinelli, A., Rogers, A. and Jennings, N. R. Decentralised Coordination of Mobile Sensors Using the Max-Sum Algorithm, IJCAI-09

Main Technical Contribution

Activation Time Heading and Velocity Desired Temperature

Main Issues:• Representation: how do we

represent continuous utilities?• Operations: need to redefine main

operations of max-sum: • Max-marginalisation• Addition

Application Domain: Coordinate duty cycles of energy aware sensors to maximise event detection probability

Representation: Continuous Piece-Wise Linear functions

Max-marginalisation: 1. Project 2. Extract upper envelope

Addition: 1. Merge domains2. Add values

• Stranders, R., Farinelli, A., Rogers, A. and Jennings, N. R. Decentralised Coordination of Continuously Valued Control Parameters using the Max-Sum Algorithm, AAMAS-08