Efficient Spectral Control of Partially Observed Linear Dynamical Systems
This work addresses efficient control in partially observed linear systems, offering significant computational improvements for applications in robotics or autonomous systems, though it appears incremental as it builds on existing regret guarantees.
The paper tackles the problem of controlling linear dynamical systems under partial observation and adversarial disturbances, proposing the Double Spectral Control (DSC) algorithm that matches best known regret guarantees while exponentially improving runtime complexity in terms of the system's stability margin.
We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while exponentially improving runtime complexity over previous approaches in its dependence on the system's stability margin. Our key innovation is a two-level spectral approximation strategy, leveraging double convolution with a universal basis of spectral filters, enabling efficient and accurate learning of the best linear dynamical controllers.