Toward a Systems Theory of Algorithms

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an in silico existence. However, this perspective is inappropriate for many modern computational approaches in control, learning, or optimization, wherein in vivo algorithms interact with their environment. Examples of such open algorithms include various real-time optimization-based control strategies, reinforcement learning, decision-making architectures, online optimization, and many more. Further, even closed algorithms in learning or optimization are increasingly abstracted in block diagrams with interacting dynamic modules and pipelines. In this opinion letter, we state our vision on a to-be-cultivated 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 rangeofchallenges 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.