arXiv subjects

Riccardo Cescon

Publications and source records attributed to Riccardo Cescon.

3 recordsLinked to original sources

arXiv2026

Sinkhorn Ambiguity Sets for Distributionally Robust Control: Convexity, Weak Compactness, and Tractability

Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC) problem with ambiguity sets defined via the Sinkhorn discrepancy. Compared to other discrepancy measures based on optimal transport, such as the popular Wasserstein distance, the Sinkhorn divergence does not constrain the worst-case distribution to be discrete, and allows combining observed data with prior knowledge in the form of a reference distribution, making this choice particularly suitable when only few noise samples are available for control design. We first study the properties of Sinkhorn ambiguity sets, establishing convexity and weak compactness under standard assumptions. We then leverage these results to prove that, the Sinkhorn DR linear quadratic control problem over linear policies can be solved through convex programming-even in the presence of DR safety constraints. Finally, we validate our theoretical findings and demonstrate the effectiveness of the proposed approach on a trajectory planning example.

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arXiv2025

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

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.

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arXiv2025

Data-driven Distributionally Robust Control Based on Sinkhorn Ambiguity Sets

As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework for decision-making under distributional uncertainty only using noise samples. However, while the resulting policies inherit strong probabilistic guarantees when the number of samples is sufficiently high, their performance may significantly degrade when only a few data are available. Inspired by recent results from the machine learning community, we introduce an entropic regularization to penalize deviations from a given reference distribution and study data-driven DR control over Sinkhorn ambiguity sets. We show that for finite-horizon control problems, the optimal DR linear policy can be computed via convex programming. By analyzing the relation between the ambiguity set defined in terms of Wasserstein and Sinkhorn discrepancies, we reveal that, as the regularization parameter increases, this optimal policy interpolates between the solution of the Wasserstein DR problem and that of the stochastic problem under the reference distribution. We validate our theoretical findings and the effectiveness of our approach when only scarce data are available on a numerical example.

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