Decentralised Coordination through Local Message Passing Alex Rogers School of Electronics and Computer Science University of Southampton

Overview Decentralised Coordination Landscape of Algorithms –Optimality vs Communication Costs Local Message Passing Algorithms –Max-sum algorithm –Graph Colouring Example Application –Wide Area Surveillance Scenario Future Work

Decentralised Coordination Agents Multiple conflicting goals and objectives Discrete set of possible actions Some locality of interaction

Decentralised Coordination Agents Maximise Social Welfare:

Decentralised Coordination Agents Central point of control No direct communication Solution scales poorly Central point of failure Who is the centre?

Decentralised Coordination Agents Decentralised control and coordination through local computation and message passing. Speed of convergence, guarantees of optimality, communication overhead, computability

Landscape of Algorithms Complete Algorithms DPOP OptAPO ADOPT Communication Cost Optimality Iterative Algorithms Best Response (BR) Distributed Stochastic Algorithm (DSA) Fictitious Play (FP) Greedy Heuristic Algorithms Predictive Algorithms Dr. David Leslie Archie Chapman Michalis Smyrnakis Maike Kaufmann Dr. George Loukas Probability Collectives Message Passing Algorithms Sum-Product Algorithm

Sum-Product Algorithm Variable nodes Function nodes Factor Graph A simple transformation: allows us to use the same algorithms to maximise social welfare: Find approximate solutions to global optimisation through local computation and message passing:

Graph Colouring Graph Colouring ProblemEquivalent Factor Graph

Graph Colouring Equivalent Factor Graph Utility Function

Optimality

Communication Cost

Robustness to Message Loss

Wide Area Surveillance Scenario Dense deployment of sensors to detect pedestrian and vehicle activity within an urban environment. Unattended Ground Sensor

Energy Constrained Sensors Maximise event detection whilst using energy constrained sensors: –Use sense/sleep duty cycles to maximise network lifetime of maintain energy neutral operation. –Coordinate sensors with overlapping sensing fields. time duty cycle t ime duty cycle

Energy-Aware Sensor Networks

Applications Combat Management System Insyte Coordinating Mobile Sensors Ruben Stranders

Future Work Continuous action spaces –Max-sum calculations are not limited to discrete action space –Can we perform the standard max-sum operators on continuous functions in a computationally efficient manner? Bounded Solutions –Max-sum is optimal on tree and limited proofs of convergence exist for cyclic graphs –Can we construct a tree from the original cyclic graph and calculate an lower bound on the solution quality?