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In this paper, a mixed-integer linear programming formulation for the problemof obtaining task-relevant, multi-resolution, graph abstractions forresource-constrained agents is presented. The formulation leverages conceptsfrom information-theoretic signal compression, specifically the informationbottleneck (IB) method, to pose a graph abstraction problem as an optimalencoder search over the space of multi-resolution trees. The abstractionsemerge in a task-relevant manner as a function of agent information-processingconstraints, and are not provided to the system a priori. We detail ourformulation and show how the problem can be realized as an integer linearprogram. A non-trivial numerical example is presented to demonstrate theutility in employing our approach to obtain hierarchical tree abstractions forresource-limited agents.

Information-Theoretic Abstractions for Resource-Constrained Agents via Mixed-Integer Linear Programming