Regret-Optimal Linear-Quadratic Control under Distributional Drift
Abstract
We study finite-horizon LQR with independent disturbances whose laws may drift over time. We address uncertainty in this evolution through ex-ante distributionally robust regret optimization (DRRO), which minimizes worst-case excess expected cost relative to the optimal causal controller that knows the law sequence. To specify the admissible law sequences, we introduce a temporally coupled moment ambiguity set with a Gelbrich kinetic-energy budget and a second budget limiting departures from reference moments and persistent cumulative mismatch. Despite the coupling of moments across time, affine disturbance-feedback synthesis reduces exactly to a semidefinite program. An optimal policy uses past disturbances to predict the correction to nominal LQR determined by current and future disturbance means. The SDP solution also yields worst-case moment paths and corresponding laws. For standard distributionally robust optimization (DRO), the analogous SDP relaxation can have a duality gap. Portfolio liquidation experiments show substantially lower worst-case regret over the drifting ambiguity set than common-law DRRO and nominal control.
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BibTeX
@misc{fiechtner2026regretoptimal,
title = {{Regret-Optimal Linear-Quadratic Control under Distributional Drift}},
author = {Lukas-Benedikt Fiechtner and Jose Blanchet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09220},
eprint = {2610.09220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09220},
}
RIS
TY - UNPB
TI - Regret-Optimal Linear-Quadratic Control under Distributional Drift
AU - Lukas-Benedikt Fiechtner
AU - Jose Blanchet
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09220
UR - https://arxiv.org/abs/2610.09220
AB - We study finite-horizon LQR with independent disturbances whose laws may drift over time. We address uncertainty in this evolution through ex-ante distributionally robust regret optimization (DRRO), which minimizes worst-case excess expected cost relative to the optimal causal controller that knows the law sequence. To specify the admissible law sequences, we introduce a temporally coupled moment ambiguity set with a Gelbrich kinetic-energy budget and a second budget limiting departures from reference moments and persistent cumulative mismatch. Despite the coupling of moments across time, affine disturbance-feedback synthesis reduces exactly to a semidefinite program. An optimal policy uses past disturbances to predict the correction to nominal LQR determined by current and future disturbance means. The SDP solution also yields worst-case moment paths and corresponding laws. For standard distributionally robust optimization (DRO), the analogous SDP relaxation can have a duality gap. Portfolio liquidation experiments show substantially lower worst-case regret over the drifting ambiguity set than common-law DRRO and nominal control.
ER -