Download
1 / 7
70 likes | 83 Views
This emerging area focuses on decentralized detection in complex networks, addressing local and global objectives while organizing sensing nodes to generate and interpret messages. The optimal design requires careful thought to avoid the traps of optimality, such as various communication constraints and decision-making protocols. Two algorithmic structures, Gauss-Seidel and Jacobi, are explored for iterative optimization of local decision rules, involving message passing and cost-to-go calculations. Understand the complexities of choosing decision "rules" and specifying graph models, considering the underlying phenomenon, the sensor network, and associated costs. Dive into the intricacies of globally compatible rules and intractable optimization challenges, especially when nodes can request information in a network coordination context.
E N D
Network coordination and communication/fusion protocols based on team-theoretic principals Final MURI Review Meeting Alan S. Willsky December 2, 2005
How can we take objectives of other nodes into account? • Rapprochement of two lines of inquiry • Decentralized detection • Message passing algorithms for graphical models • This is an emergingarea, not a mature one: • When there are communications constraints and both local and global objectives, optimal design requires the sensing nodes to organize • Who does what? • How can other nodes best help? • This organization in essence specifies a protocol for generating and interpreting messages • Avoiding the traps of optimality for decentralized detection for complex networks requires careful thought
A tractable and instructive case • Directed set of sensing/decision nodes • Each node has its local measurements • Each node receives one or more bits of information from its “parents” and sends one or more bits to its “children” • Overall cost is a sum of costs incurred by each node based on the bits it generates and the value of the state of the phenomenon being measured • Each node has a local model of the part of the underlying phenomenon that it observes and for which it is responsible • Simplest case: the phenomenon being measured has graph structure compatible with that of the sensing nodes
Person-by-person optimal solution • Iterative optimization of local decision rules: A message-passing algorithm! • Each local optimization step requires • A pdf for the bits received from parents (based on the current decision rules at ancestor nodes) • A cost-to-go summarizing the impact of different decisions on offspring nodes based on their current decision rules
Two algorithmic structures • Gauss-Seidel, e.g. sweeping from one end to the other and then back • Convergence guaranteed, as cost reduced at each stage • Very particular message scheduling • Jacobi—Everyone updates at the same time • No convergence guarantees, but has same equilibria • Corresponds to the simplest message passing structure in BP: Everyone sends and receives messages at each iteration
Reverse Pass: “Receive, Update & Send” Forward Pass: “Receive & Send” m6,10 m10,6 6 m46 m64 1 10 10 10 m14 m41 9 7 6 2 4 5 3 1 8 3 5 4 8 2 6 7 9 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 m7,11 m11,7 4 7 1 1 m47 m74 m25 m52 11 11 2 11 0 0 1 1 m58 m85 5 8 m8,11 m11,8 1 1 3 m35 m53 12 12 12 1 m59 m95 0 0 1 9 m9,12 1 m12,9 1 2 3 7 6 5 4 3 2 1 Message-Passing Algorithm: Example Initialization: Myopic Strategy
What happens with more general networks? • Choosing decision “rules” corresponds to specifying a graphical model consisting of • The underlying phenomenon • The sensor network (the part of the model we get to play with) • The cost • There are nontrivial issues in specifying globally compatible decision “rules” • Optimization (and for that matter cost evaluation) is intractable, for exactly the same reasons as inference for graphical models • The problem is even more complex if nodes can request information (even no news is news)
