Data-Driven Inverse Reinforcement Learning of Linear Systems with Model Uncertainty: A Convex Optimization View
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| Format: | Preprint |
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2026
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| author | Nguyen, Duc Cuong Dao, Phuong Nam |
| author_facet | Nguyen, Duc Cuong Dao, Phuong Nam |
| contents | Inverse reinforcement learning (IRL) for linear systems seeks a cost function whose optimal controller reproduces an expert policy from data. Existing data-driven methods for discrete-time linear systems are largely built on iterative policy/value updates, repeated matrix inversions, and, in some cases, an initial stabilizing controller, which can limit numerical robustness and practical applicability. This paper develops a convex-optimization framework for data-driven inverse reinforcement learning of discrete-time linear systems with model uncertainty. For nominal systems, we derive a semidefinite characterization of inverse optimality and a relaxed formulation that recovers an equivalent state-cost matrix together with a stabilizing controller from expert trajectories. We then obtain a model-free, off-policy reformulation by replacing the unknown system matrices with a regressed kernel matrix identified from local input--state data. For uncertain local systems, we show that a standard LQR cost is generally insufficient to represent every stabilizing target gain and therefore introduce a generalized LQR cost with a state--input cross term. Based on this model, we develop a convex data-driven inverse-RL method and extend it to robust cost design over a population of perturbations via differentiable semidefinite programming and stochastic approximation. Simulations on a discrete-time power-system example show accurate recovery of expert behavior, improved robustness to gain-estimation error and model mismatch, and a simpler computational pipeline than classical iterative inverse-RL schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-Driven Inverse Reinforcement Learning of Linear Systems with Model Uncertainty: A Convex Optimization View Nguyen, Duc Cuong Dao, Phuong Nam Systems and Control Inverse reinforcement learning (IRL) for linear systems seeks a cost function whose optimal controller reproduces an expert policy from data. Existing data-driven methods for discrete-time linear systems are largely built on iterative policy/value updates, repeated matrix inversions, and, in some cases, an initial stabilizing controller, which can limit numerical robustness and practical applicability. This paper develops a convex-optimization framework for data-driven inverse reinforcement learning of discrete-time linear systems with model uncertainty. For nominal systems, we derive a semidefinite characterization of inverse optimality and a relaxed formulation that recovers an equivalent state-cost matrix together with a stabilizing controller from expert trajectories. We then obtain a model-free, off-policy reformulation by replacing the unknown system matrices with a regressed kernel matrix identified from local input--state data. For uncertain local systems, we show that a standard LQR cost is generally insufficient to represent every stabilizing target gain and therefore introduce a generalized LQR cost with a state--input cross term. Based on this model, we develop a convex data-driven inverse-RL method and extend it to robust cost design over a population of perturbations via differentiable semidefinite programming and stochastic approximation. Simulations on a discrete-time power-system example show accurate recovery of expert behavior, improved robustness to gain-estimation error and model mismatch, and a simpler computational pipeline than classical iterative inverse-RL schemes. |
| title | Data-Driven Inverse Reinforcement Learning of Linear Systems with Model Uncertainty: A Convex Optimization View |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.09164 |