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arXiv · 2609.27653

Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise

Jakob Nylöf·Daniel Kuhn·John Lygeros·Giancarlo Ferrari-Trecate
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Abstract

We study finite-horizon distributionally robust linear-quadratic control with disturbances that can be arbitrarily correlated in time. The ambiguity set is modeled as a single 2-Wasserstein ball centered at a nominal elliptically contoured distribution of the disturbances. Despite the infinite-dimensionality of both the policy space and ambiguity set, we prove that the optimal policy is affine and that the worst-case distribution is an affine push-forward of the nominal distribution. These affine maps can be computed efficiently via a best-response algorithm based on the Frank--Wolfe algorithm. Experiments demonstrate improved out-of-sample performance over LQG and its distributionally robust extensions when the true disturbances are correlated, incurring only a small loss of performance under uncorrelated disturbances.

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Jakob Nylöf, Daniel Kuhn, John Lygeros, Giancarlo Ferrari-Trecate. 2026-09-23. Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise. https://arxiv.org/abs/2609.27653

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