Towards a Systems Theory of Algorithms
Florian Dörfler Zhiyu He Giuseppe Belgioioso Saverio Bolognani John Lygeros Michael Muehlebach
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} 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
favour 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 also provide valuable
insights into this burgeoning paradigm shift and its accompanying challenges in
the algorithmic world. We survey various instances where the principles of
algorithmic systems theory are being developed and outline pertinent modeling,
analysis, and design challenges.