Information-Theoretic Abstractions for Resource-Constrained Agents via Mixed-Integer Linear Programming
This addresses the challenge of enabling resource-limited agents to efficiently process information in complex environments, though it appears incremental as it applies existing information-theoretic concepts to a specific formulation.
The paper tackles the problem of generating task-relevant, multi-resolution graph abstractions for resource-constrained agents by formulating it as a mixed-integer linear programming problem based on the information bottleneck method, and demonstrates its utility through a non-trivial numerical example.
In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically the information bottleneck (IB) method, to pose a graph abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints, and are not provided to the system a priori. We detail our formulation and show how the problem can be realized as an integer linear program. A non-trivial numerical example is presented to demonstrate the utility in employing our approach to obtain hierarchical tree abstractions for resource-limited agents.