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.

翻译：传统上，数值算法被视为局限于数字计算环境的孤立代码片段。然而，这一视角并不适用于控制、学习或优化领域中许多现代计算方法，在这些方法中，体内算法会与其环境进行交互。此类开放算法的示例包括各种基于实时优化的控制策略、强化学习、决策架构、在线优化等。此外，即使学习或优化中的封闭算法也越来越多地通过具有交互动态模块与管道的框图来抽象表示。在这篇观点论文中，我们阐述了对有待培养的“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、人类或数据库进行交互的开放动态系统。值得注意的是，在系统理论框架下发展出的多种工具也为算法世界中这种新兴范式转变及其伴随的挑战提供了宝贵见解。我们综述了算法系统理论原则正在发展的各种实例，并概述了相关的建模、分析与设计挑战。