Characterizing Identifiability and Generalization for Inverse Receding-Horizon Linear-Quadratic Regulator Problems
Abstract
We consider the problem of objective inference in the context of receding-horizon linear-quadratic regulator (LQR). In this setting, we are given sequential state-action observations, where each observed action is the first control of a newly solved finite-horizon LQR problem. We characterize when the objective of that problem is uniquely identifiable from these observations and when additional observations provide no new information about the objective. We then analyze action prediction at unseen states and show that all objectives reproducing the observed actions yield identical actions throughout the affine hull of the observed states; outside this hull, we derive an upper bound on the prediction error. % and deriving a prediction-error bound outside this hull. Additionally, we show that, when only the linear objective terms are unknown, exact prediction holds at every state. Finally, numerical results show that, even under stochastic observation noise, re-optimizing an inferred objective enables accurate action prediction at unseen states across different planning horizons.
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BibTeX
@misc{jin2026characterizing,
title = {{Characterizing Identifiability and Generalization for Inverse Receding-Horizon Linear-Quadratic Regulator Problems}},
author = {Zhiyuan Jin and Jingqi Li and David Fridovich-Keil},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14053},
eprint = {2609.14053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14053},
}
RIS
TY - UNPB
TI - Characterizing Identifiability and Generalization for Inverse Receding-Horizon Linear-Quadratic Regulator Problems
AU - Zhiyuan Jin
AU - Jingqi Li
AU - David Fridovich-Keil
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14053
UR - https://arxiv.org/abs/2609.14053
AB - We consider the problem of objective inference in the context of receding-horizon linear-quadratic regulator (LQR). In this setting, we are given sequential state-action observations, where each observed action is the first control of a newly solved finite-horizon LQR problem. We characterize when the objective of that problem is uniquely identifiable from these observations and when additional observations provide no new information about the objective. We then analyze action prediction at unseen states and show that all objectives reproducing the observed actions yield identical actions throughout the affine hull of the observed states; outside this hull, we derive an upper bound on the prediction error. % and deriving a prediction-error bound outside this hull. Additionally, we show that, when only the linear objective terms are unknown, exact prediction holds at every state. Finally, numerical results show that, even under stochastic observation noise, re-optimizing an inferred objective enables accurate action prediction at unseen states across different planning horizons.
ER -