New math shows why some control systems are fundamentally hard to learn
Researchers have proven that certain industrial control systems require exponentially more time and data to master than others. The findings establish hard limits on how fast autonomous systems can adapt—knowledge that matters for manufacturing, robotics, and energy grids where learning speed directly affects profitability and safety.
Originaltitel: Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems
<p>In this article, we establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs. We combine ideas from experiment design, estimation theory, and a perturbation bound of certain information matrices to derive regret lower bounds exhibiting scaling on the order of magnitude root T in the time horizon T . Our bounds accurately capture the role of control-theoretic parameters and we are able to show that systems that are hard to control are also hard to learn to control; when instantiated to state feedback systems we recover the dimensional dependency of earlier work but with improved scaling with system-theoretic constants, such as system costs and Gramians. Furthermore, we extend our results to a class of partially observed systems and demonstrate that systems with poor observability structure also are hard to learn to control.</p>