# Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach

arXiv: https://arxiv.org/abs/2608.05953 · HTML: https://mlsanity.com/paper/2608.05953/

## 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.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 6 of 6)

- [Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method](https://mlsanity.com/paper/2011.14516/) (2020)
- [Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Control](https://mlsanity.com/paper/2212.02072/) (2022)
- [The Duality of Generative AI and Reinforcement Learning in Robotics: A Review](https://mlsanity.com/paper/2410.16411/) (2024)
- [On stabilizability and exact observability of stochastic systems with their applications](https://mlsanity.com/paper/2307.08915/) (2023)
- [Scaling policy iteration based reinforcement learning for unknown discrete-time linear systems](https://mlsanity.com/paper/2411.07825/) (2024)
- [Cooperative Optimal Output Tracking for Discrete-Time Multiagent Systems: Stabilizing Policy Iteration Frameworks](https://mlsanity.com/paper/2501.06510/) (2025)

## 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.