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The Algorithmic Regulator

Created by
  • Haebom

Author

Giulio Ruffini

Outline

This paper analyzes control problems from the perspective of Algorithmic Information Theory (AIT), building on the regulator theorem, which states that, under certain conditions, an optimal controller must embed a model of the system it controls. The authors treat a closed deterministic system as a single program and define a "good algorithmic regulator" by measuring the degree to which the controller reduces the algorithmic complexity of its output. The paper proves that a world-regulator pair with higher mutual algorithmic information is preferred as the algorithmic complexity reduction ($\Delta$) increases. In other words, the idea that the regulator must "embed" a model of the world is quantified based on AIT. Furthermore, this framework is distribution-independent, applicable to individual sequences, and complements the internal model principle. Consequently, the controller behaves as if it were minimizing the conditional description length, suggesting the role of a standard scalar objective and planner.

Takeaways, Limitations

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Takeaways:
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We rigorously demonstrate and quantitatively explain the idea that regulators must embed a model of the world through AIT.
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It addresses control problems in a distribution-independent manner, making it applicable to a variety of situations.
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We show that in a single episode, the controller behaves as if it were minimizing the conditional description length.
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It presents a new perspective on control theory by implying the role of standard scalar goals and planners.
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Limitations:
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Because the calculation of algorithmic complexity is incomputable, it may be difficult to apply in practical applications.
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Because the regulator theorem has only been proven in a limited environment, further research is needed to extend it to general situations.
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The paper lacks specific examples of specific applications or actual control system design.
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