# Data-Driven Inverse Reinforcement Learning of Linear Systems with Model Uncertainty: A Convex Optimization View

arXiv: https://arxiv.org/abs/2605.09164 · HTML: https://mlsanity.com/paper/2605.09164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 0 of its 18 references that are in the map.
- First posted on arXiv 9 May 2026.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)
- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Abstract (arXiv)

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.