Connecting control theory and machine learning for smarter systems
Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
Machine Learning
Summary
Complex data is hard to understand and use, so the authors highlight how ideas from physics, math, and machine learning come together to help. They show that five areas—control, transport, inference, thermodynamics, and machine learning—share a common goal: optimizing certain mathematical functions under constraints. This connection allows for new ways to improve learning methods like reinforcement learning and generating models. The paper explains these links in simple terms starting from basic physics ideas.
What this means in practice
- •For reinforcement learning engineers: Use thermodynamics-based optimization principles to improve decision-making algorithms in reinforcement learning systems.
- •For machine learning model developers: Incorporate connections between transport and inference theories to enhance generative and variational models for better data synthesis and understanding.
A survey. It maps existing work.
Authors
Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin
Abstract
The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.