Efficient Spectral Control of Partially Observed Linear Dynamical Systems

TL;DR

This paper introduces Double Spectral Control (DSC), an efficient algorithm for controlling partially observed linear dynamical systems with adversarial disturbances, achieving optimal regret with significantly improved runtime.

Contribution

The paper presents a novel two-level spectral approximation strategy that enhances computational efficiency in learning optimal controllers for linear dynamical systems.

Findings

Matches best known regret guarantees

Exponential runtime complexity improvement

Efficient learning of linear controllers

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.