Towards a Systems Theory of Algorithms

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization, wherein {\em in vivo} algorithms interact with their environm...

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Published in:arXiv.org
Main Authors: Dörfler, Florian, He, Zhiyu, Belgioioso, Giuseppe, Bolognani, Saverio, Lygeros, John, Muehlebach, Michael
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 30.04.2024
Subjects:
Algorithms
Block diagrams
Dynamical systems
Machine learning
Optimization
System theory
Systems theory
ISSN:2331-8422
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Abstract Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization, wherein {\em in vivo} algorithms interact with their environment. Examples of such {\em open algorithms} include various real-time optimization-based control strategies, reinforcement learning, decision-making architectures, online optimization, and many more. Further, even {\em closed} algorithms in learning or optimization are increasingly abstracted in block diagrams with interacting dynamic modules and pipelines. In this opinion paper, we state our vision on a to-be-cultivated {\em systems theory of algorithms} and argue in favor of viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Remarkably, the manifold tools developed under the umbrella of systems theory are well suited for addressing a range of challenges in the algorithmic domain. We survey various instances where the principles of algorithmic systems theory are being developed and outline pertinent modeling, analysis, and design challenges.
AbstractList Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization, wherein {\em in vivo} algorithms interact with their environment. Examples of such {\em open algorithms} include various real-time optimization-based control strategies, reinforcement learning, decision-making architectures, online optimization, and many more. Further, even {\em closed} algorithms in learning or optimization are increasingly abstracted in block diagrams with interacting dynamic modules and pipelines. In this opinion paper, we state our vision on a to-be-cultivated {\em systems theory of algorithms} and argue in favor of viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Remarkably, the manifold tools developed under the umbrella of systems theory are well suited for addressing a range of challenges in the algorithmic domain. We survey various instances where the principles of algorithmic systems theory are being developed and outline pertinent modeling, analysis, and design challenges.
Author Lygeros, John
Bolognani, Saverio
He, Zhiyu
Muehlebach, Michael
Dörfler, Florian
Belgioioso, Giuseppe
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Snippet Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate...
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Block diagrams
Dynamical systems
Machine learning
Optimization
System theory
Systems theory
Title Towards a Systems Theory of Algorithms
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