Efficient Spectral Control of Partially Observed Linear Dynamical Systems

Anand Paresh Brahmbhatt, Gon Buzaglo, Sofiia Druchyna, Elad Hazan

Keywords: Online Convex Optimization, Online Control, Linear Dynamical Systems

TL;DR: We give a new algorithm for online control of partially observed LDS based on spectral filtering with exponential improvement in running time.

Abstract: 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.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 8369