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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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Cite

BibTeXRIS
BibTeX
@misc{nylof2026optimality,
  title = {{Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise}},
  author = {Jakob Nylöf and Daniel Kuhn and John Lygeros and Giancarlo Ferrari-Trecate},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27653},
  eprint = {2609.27653},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27653},
}
RIS
TY  - UNPB
TI  - Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise
AU  - Jakob Nylöf
AU  - Daniel Kuhn
AU  - John Lygeros
AU  - Giancarlo Ferrari-Trecate
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27653
UR  - https://arxiv.org/abs/2609.27653
AB  - 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.
ER  -