Efficient Spectral Control of Partially Observed Linear Dynamical Systems Anand Brahmbhatt1 Gon Buzaglo1 Sofiia Druchyna1 Elad Hazan1,2

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.