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We consider the problem of decentralized sequential active hypothesis testing (DSAHT), where two transmitting agents, each possessing a private message, are actively helping a third agent–and each other–to learn the message pair over a discrete memoryless multiple access channel (DM-MAC). The third agent (receiver) observes the noisy channel output, which is also available to the transmitting agents via noiseless feedback. We formulate this problem as a decentralized dynamic team, show that optimal transmission policies have a time-invariant domain, and characterize the solution through a dynamic program. Several alternative formulations are discussed involving time-homogenous cost functions and/or variable-length codes, resulting in solutions described through fixed-point, Bellman-type equations. Subsequently, we make connections with the problem of simplifying the multi-letter capacity expressions for the noiseless feedback capacity of the DM-MAC. We show that restricting attention to distributions induced by optimal transmission schemes for the DSAHT problem, without loss of optimality, transforms the capacity expression, so that it can be thought of as the average reward received by an appropriately defined stochastic dynamical system with time-invariant state space.
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Optimal Threshold-Based Distributed Control Policies for Persistent Monitoring on Graphs
We consider the optimal multi-agent persistent monitoring problem defined by a team of cooperating agents visiting a set of nodes (targets) on a graph with the objective of minimizing a measure of overall node state uncertainty. The solution to this problem involves agent trajectories defined both by the sequence of nodes to be visited by each agent and the amount of time spent at each node. We propose a class of distributed threshold-based parametric controllers through which agent transitions from one node to the next are controlled by thresholds on the node uncertainty. The resulting behavior of the agent-target system is described by a hybrid dynamic system. This enables the use of Infinitesimal Perturbation Analysis (IPA) to determine on-line optimal threshold parameters through gradient descent and thus obtain optimal controllers within this family of threshold-based policies. Simulations are included to illustrate our results and compare them to optimal solutions derived through dynamic programming.
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- PAR ID:
- 10122831
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 0743-1619
- Page Range / eLocation ID:
- 2030-2035
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
