Proximal algorithms for large-scale statistical modeling and sensor/actuator selection
This work addresses computational bottlenecks in large-scale statistical modeling and control for applications like sensor networks or system optimization, though it is incremental as it builds on existing proximal methods.
The paper tackles the challenge of modeling and controlling large-scale stochastically-driven dynamical systems by formulating problems like statistical modeling and sensor/actuator selection as regularized semi-definite programs. It develops a unified proximal algorithm framework that enables handling these problems at substantially larger scales than current solvers, with demonstrated linear convergence and effectiveness in examples.
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework.