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

2021-02-19 16:34:47
Daniel T. Larsson, Dipankar Maity, Panagiotis Tsiotras
arXiv_AI
       
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.

Abstract (translated)

URL

https://arxiv.org/abs/2102.10015

PDF

https://arxiv.org/pdf/2102.10015.pdf

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