Towards a Systems Theory of Algorithms

Towards a Systems Theory of Algorithms

30 Apr 2024 | Florian Dörfler*, Zhiyu He*,†, Giuseppe Belgioioso*, Saverio Bolognani*, John Lygeros*, & Michael Muehlebach†
The paper "Towards a Systems Theory of Algorithms" by Florian Dörfler, Zhiyu He, Giuseppe Belgiioso, Saverio Bolognani, John Lygeros, and Michael Muehlebach advocates for a systems theory perspective on algorithms, viewing them as open dynamical systems interacting with their environment. The authors argue that traditional views of algorithms as isolated pieces of code are insufficient for modern computational approaches in control, learning, and optimization. They propose that algorithms should be understood as interconnected systems, similar to how control systems are analyzed and designed using systems theory. The paper highlights the importance of systems theory in addressing the challenges of modern algorithms, such as real-time optimization, reinforcement learning, and decision-making architectures. It emphasizes the need to consider algorithms as open systems with inputs, outputs, and internal states, and to analyze their interactions with other systems, including physical and human systems. Key messages from the paper include: 1. **Abstraction and Modularity**: Systems theory provides a powerful framework for abstracting algorithms into block diagrams, breaking down complexity and enabling the study of feedback, uncertainty, and dynamic interactions. 2. **Analysis and Design**: Concepts from systems theory, such as time-scale separation, system gains, and small-gain theorems, are useful for analyzing and designing algorithms, especially when they interact with other systems. 3. **Performance Beyond Convergence**: Systems theory allows for a broader analysis of algorithm performance, including disturbance rejection, regret, and architectural design, which are crucial for real-world applications. The paper also provides several examples to illustrate the application of systems theory to optimization algorithms, machine learning, and real-time algorithms in feedback loops. These examples demonstrate how systems theory can enhance the analysis and design of complex algorithms, leading to more robust and efficient solutions. Finally, the authors suggest that the systems theory perspective can be applied to decision-making architectures, particularly in control systems, to address challenges such as system boundaries, interacting components, and tolerable uncertainty. They emphasize the potential of systems theory to provide new insights into phenomena like performative prediction and data-driven predictive control.The paper "Towards a Systems Theory of Algorithms" by Florian Dörfler, Zhiyu He, Giuseppe Belgiioso, Saverio Bolognani, John Lygeros, and Michael Muehlebach advocates for a systems theory perspective on algorithms, viewing them as open dynamical systems interacting with their environment. The authors argue that traditional views of algorithms as isolated pieces of code are insufficient for modern computational approaches in control, learning, and optimization. They propose that algorithms should be understood as interconnected systems, similar to how control systems are analyzed and designed using systems theory. The paper highlights the importance of systems theory in addressing the challenges of modern algorithms, such as real-time optimization, reinforcement learning, and decision-making architectures. It emphasizes the need to consider algorithms as open systems with inputs, outputs, and internal states, and to analyze their interactions with other systems, including physical and human systems. Key messages from the paper include: 1. **Abstraction and Modularity**: Systems theory provides a powerful framework for abstracting algorithms into block diagrams, breaking down complexity and enabling the study of feedback, uncertainty, and dynamic interactions. 2. **Analysis and Design**: Concepts from systems theory, such as time-scale separation, system gains, and small-gain theorems, are useful for analyzing and designing algorithms, especially when they interact with other systems. 3. **Performance Beyond Convergence**: Systems theory allows for a broader analysis of algorithm performance, including disturbance rejection, regret, and architectural design, which are crucial for real-world applications. The paper also provides several examples to illustrate the application of systems theory to optimization algorithms, machine learning, and real-time algorithms in feedback loops. These examples demonstrate how systems theory can enhance the analysis and design of complex algorithms, leading to more robust and efficient solutions. Finally, the authors suggest that the systems theory perspective can be applied to decision-making architectures, particularly in control systems, to address challenges such as system boundaries, interacting components, and tolerable uncertainty. They emphasize the potential of systems theory to provide new insights into phenomena like performative prediction and data-driven predictive control.
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