A New Approach to Controlling Linear Dynamical Systems
This work addresses control challenges in systems with adversarial conditions, offering a more efficient algorithm for applications like robotics or autonomous systems, though it appears incremental as it builds on prior methods with specific improvements.
The authors tackled the problem of controlling linear dynamical systems under adversarial disturbances and cost functions, achieving a running time that scales polylogarithmically with the inverse stability margin, improving upon prior polynomial dependence while maintaining regret guarantees.
We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.