# Inverse Optimal Control for Linear Quadratic Problem with Poisson Jumps: Model-Free Inverse Reinforcement Learning Approaches

arXiv: https://arxiv.org/abs/2607.03169 · HTML: https://mlsanity.com/paper/2607.03169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 3 of 3)

- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Inverse reinforcement learning by expert imitation for the stochastic linear-quadratic optimal control problem](https://mlsanity.com/paper/2405.17085/) (2024)
- [Data-Driven Inverse Reinforcement Learning for Expert-Learner Zero-Sum Games](https://mlsanity.com/paper/2301.01997/) (2023)

## Abstract (arXiv)

This paper addresses the inverse optimal control (IOC) problem for stochastic linear systems subject to both Brownian motion and Poisson jumps, using an inverse reinforcement learning (IRL) framework. Given a target feedback gain from an expert, the objective is to identify an equivalent cost functional-specifically, the set of all cost weights-that yields this same gain. To solve this problem when system dynamics are unknown, we propose two model-free, off-policy IRL algorithms that operate entirely from data, circumventing the need to solve the generalized algebraic Riccati equation or compute the cost weights analytically. The first is an inverse Q-learning algorithm that constructs data-driven equations from expert demonstrations to compute the Q-function matrix, with equivalent cost weights updated algebraically and without requiring additional trajectory data. The second is a model-free off-policy inverse policy iteration algorithm that leverages data collected under an initial stabilizing policy, offering a complementary approach suited to different data availability scenarios. Crucially, by decoupling the data-collection behavior policies from the policies being iteratively updated, both algorithms can learn equivalent cost weights from sufficiently excited trajectories without identifying the system dynamics or jump intensity. Numerical simulations validate the effectiveness of the proposed methods.