6 papers
Stochastic Gradient Descent with Momentum: Analysis and Synthesis via Integral Quadratic Constraints
Dennis Gramlich, Carsten W. Scherer, Christian Ebenbauer
This article applies dynamic integral quadratic constraints (IQCs) to the analysis and synthesis of accelerated stochastic gradient algorithms. We consider composite objective func…
Global Stability and Step Size Robustness of RMSProp
Naum Dimitrieski, Maria Christine Honecker, Carsten Scherer +1
In this paper, an input-to-state Lyapunov function for the RMSProp optimization algorithm is introduced. Global asymptotic stability of the RMSProp algorithm for constant step size…
Structure, Analysis, and Synthesis of First-Order Algorithms
Jared Miller, Carsten Scherer, Fabian Jakob +1
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical sy…
Analysis and Synthesis of Switched Optimization Algorithms
Jared Miller, Fabian Jakob, Carsten Scherer +1
Deployment of optimization algorithms over communication networks face challenges associated with time delays and corruptions. Fixed time delays can destabilize popular gradient-ba…
Distributionally robust LMI synthesis for LTI systems
Dennis Gramlich, Shuhao Yan, Carsten W. Scherer +1
This article shows that distributionally robust controller synthesis as investigated in \cite{taskesen2024distributionally} can be formulated as a convex linear matrix inequality (…
Distributional Robustness in Output Feedback Regret-Optimal Control
Shuhao Yan, Carsten W. Scherer
This paper studies distributionally robust regret-optimal (DRRO) control with purified output feedback for linear systems subject to additive disturbances and measurement noise. Th…