On the Global Optimality of Linear Policies for Sinkhorn Distributionally Robust Linear Quadratic Control

2025/08/31 by Riccardo Cescon, Andrea E. Martin, Cescon, Riccardo +3
Computer Science · Decision Sciences · Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.00956

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this work proposes a distributionally robust generalization of the finite-horizon LQG control problem. Specifically, we assume that the noise distributions are unknown and belong to ambiguity sets defined in terms of an entropy-regularized Wasserstein distance centered at a nominal Gaussian distribution. By deriving novel bounds on this Sinkhorn discrepancy and proving structural and topological properties of the resulting ambiguity sets, we establish global optimality of linear policies. Numerical experiments showcase improved distributional robustness of our control policy.

Citations

• Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets
• Data-driven Distributionally Robust Control Based on Sinkhorn Ambiguity Sets
• Optimality of Linear Policies for Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions
• Infinite-Horizon Distributionally Robust Regret-Optimal Control
• Distributionally Robust Infinite-horizon Control: from a pool of samples to the design of dependable controllers
• On the Guarantees of Minimizing Regret in Receding Horizon
• Distributionally Robust LQG control under Distributed Uncertainty
• Distributionally Robust Linear Quadratic Control
• Regret Optimal Control for Uncertain Stochastic Systems
• Wasserstein Tube MPC with Exact Uncertainty Propagation
• Sinkhorn Distributionally Robust Optimization
• Regret-optimal Estimation and Control
• The statistical effect of entropic regularization in optimal\n transportation
• Entropy-Regularized 2-Wasserstein Distance between Gaussian Measures
• Learning Generative Models with Sinkhorn Divergences
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Distributionally Robust Stochastic Optimization with Wasserstein Distance

Related

• Optimality of Linear Policies in Distributionally Robust Linear Quadratic Control
• Distributionally Robust Linear Quadratic Control
• Optimality of Linear Policies for Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions
• Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets
• Data-driven Distributionally Robust Control Based on Sinkhorn Ambiguity Sets