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

TL;DR

This paper introduces an information-theoretic approach using mixed-integer linear programming to generate task-relevant, multi-resolution graph abstractions for resource-constrained agents, enabling hierarchical representations aligned with agent limitations.

Contribution

It presents a novel ILP formulation based on the information bottleneck principle to automatically derive hierarchical graph abstractions tailored to agent constraints.

Findings

Successfully formulates graph abstraction as an ILP problem.

Demonstrates utility with a numerical example for resource-limited agents.

Provides a method for task-relevant, multi-resolution graph abstraction generation.

Abstract

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.