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.

传统上，数值算法被视为孤立的代码，但对于现代控制、学习或优化领域的许多计算方法而言，这一视角不适用。本文提出了对正在形成的 “算法系统理论” 的愿景，并主张将算法视为与其他算法、物理系统、人类或数据库交互的开放动力系统。同时，文章还调查了正在发展中的算法系统理论的各种实例，并概述了相关的建模、分析和设计挑战。