Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach
On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization
Abstract (arXiv)
Policy iteration (PI) is an important reinforcement learning tool for solving optimal control problems which includes an initialization stage, i.e., the search for an initial stabilizing controller. However, the initialization stage typically relies on complete model information, thereby imposing substantial constraints on the initialization of model-free PI. For stochastic systems with multiplicative noise dependent on state and control, the stability is not ensured by Hurwitz conditions as in the deterministic case, but rather by a Lyapunov-type inequality that incorporates both drift and diffusion terms. Therefore, the corresponding model-free PI initialization problem is more challenging. To this end, a novel spectrum assignment method is proposed to obtain an initial stabilizer for PI in continuous-time indefinite stochastic linear quadratic control. With the help of the Lyapunov-type operator's spectrum, the original system is gradually approximated from the stable auxiliary system by adjusting a cumulative factor, thereby obtaining a stabilizing control gain. Furthermore, by leveraging system data and adjusting the cumulative factor, we design a model-free algorithm that does not rely on an initial stabilizing policy and can achieve optimal control. Finally, simulation results are provided to validate the effectiveness of the proposed methods.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods. Builds on 6 of its 26 references that are in the map. First posted on arXiv 6 Aug 2026.
Builds on
6 of 26 references.
References · 6
- 2020Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Methodcited by 11
- 2022Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Controlcited by 7
- 2024The Duality of Generative AI and Reinforcement Learning in Robotics: A Reviewcited by 6
- 2023On stabilizability and exact observability of stochastic systems with their applicationscited by 5
- 2024Scaling policy iteration based reinforcement learning for unknown discrete-time linear systemscited by 1
- 2025Cooperative Optimal Output Tracking for Discrete-Time Multiagent Systems: Stabilizing Policy Iteration Frameworkscited by 1
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2025Computing stabilizing feedback gains for stochastic linear systems via policy iteration method ↗
- 2025A Fully Data-Driven Value Iteration for Stochastic LQR: Convergence, Robustness and Stability
- 2025Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise
- 2025Model-free stochastic linear quadratic control for discrete-time systems with multiplicative and additive noises via semidefinite programming
- 2025Bootstrap Policy Iteration for Stochastic Linear Quadratic Tracking with Multiplicative Noise ↗
- 2024Data-Based Efficient Off-Policy Stabilizing Optimal Control Algorithms for Discrete-Time Linear Systems via Damping Coefficients
- 2026(Cheap) Stochastic Policy Gradient Converges with High Probability for Linear Quadratic Regulator
- 2025Sample-Efficient Model-Free Policy Gradient Methods for Stochastic LQR via Robust Linear Regression