Efficient Spectral Control of Partially Observed Linear Dynamical Systems

2025-05-27

AI Summary

We address online control of partially observable linear systems under adversarial disturbances. We propose the Dual-Spectrum Control (DSC) algorithm, introducing a novel two-layer spectral approximation framework that combines spectral filter bases with a double-convolutional structure to enable efficient and accurate controller learning, integrating online convex optimization with robust control theory. Our theoretical contributions are twofold: (i) we establish the first optimal regret bound for this setting; and (ii) we achieve exponential acceleration in computational efficiency—reducing the dependence of runtime on system stability margin from polynomial to exponential. By overcoming the inherent computational bottlenecks of conventional spectral methods while preserving strong theoretical guarantees, DSC establishes a new paradigm for robust adaptive control in high-dimensional and non-stationary environments.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Control linear dynamical systems under partial observation
• Handle adversarial disturbances in dynamical systems
• Improve runtime complexity for spectral control

Innovation

• Double Spectral Control (DSC) algorithm
• Two-level spectral approximation strategy
• Double convolution with spectral filters