An Internal Model Principle For Robots

TL;DR

This paper establishes a mathematical principle called sufficiency that enables robots to develop internal models of their environment solely from internal data, linking internal structure to environmental structure without probabilistic assumptions.

Contribution

It introduces a non-probabilistic, discrete internal model principle for robots, connecting internal system design to environmental structure through sufficiency and surprise minimization.

Findings

Sufficiency is a key mathematical condition for internal models.

Internal models can be isomorphic or bisimulation equivalent to the environment.

A connection to the free-energy principle and surprise minimization is demonstrated.

Abstract

When designing a robot's internal system, one often makes assumptions about the structure of the intended environment of the robot. One may even assign meaning to various internal components of the robot in terms of expected environmental correlates. In this paper we want to make the distinction between robot's internal and external worlds clear-cut. Can the robot learn about its environment, relying only on internally available information, including the sensor data? Are there mathematical conditions on the internal robot system which can be internally verified and make the robot's internal system mirror the structure of the environment? We prove that sufficiency is such a mathematical principle, and mathematically describe the emergence of the robot's internal structure isomorphic or bisimulation equivalent to that of the environment. A connection to the free-energy principle is established, when sufficiency is interpreted as a limit case of surprise minimization. As such, we show that surprise minimization leads to having an internal model isomorphic to the environment. This also parallels the Good Regulator Principle which states that controlling a system sufficiently well means having a model of it. Unlike the mentioned theories, ours is discrete, and non-probabilistic.