# Model-free optimal control of discrete-time systems with additive and multiplicative noises

arXiv: https://arxiv.org/abs/2008.08734 · HTML: https://mlsanity.com/paper/2008.08734/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 8 of 8)

- [Beyond Conformal Predictors: Adaptive Conformal Inference with Confidence Predictors](https://mlsanity.com/paper/2409.15548/) (2024)
- [Policy Gradient Methods for Discrete Time Linear Quadratic Regulator With Random Parameters](https://mlsanity.com/paper/2303.16548/) (2023)
- [Sample Complexity of Linear Quadratic Regulator Without Initial Stability](https://mlsanity.com/paper/2502.14210/) (2025)
- [Direct Data Driven Control Using Noisy Measurements](https://mlsanity.com/paper/2505.06407/) (2025)
- [Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise](https://mlsanity.com/paper/2506.02613/) (2025)
- [Global Convergence of Policy Gradient for Entropy Regularized Linear-Quadratic Control with Multiplicative Noise](https://mlsanity.com/paper/2510.02896/) (2025)
- [Comparative Study of Q-Learning for State-Feedback LQG Control with an Unknown Model](https://mlsanity.com/paper/2511.07870/) (2025)
- [Model-free stochastic linear quadratic control for discrete-time systems with multiplicative and additive noises via semidefinite programming](https://mlsanity.com/paper/2512.20911/) (2025)

## Abstract (arXiv)

This paper investigates the optimal control problem for a class of discrete-time stochastic systems subject to additive and multiplicative noises. A stochastic Lyapunov equation and a stochastic algebra Riccati equation are established for the existence of the optimal admissible control policy. A model-free reinforcement learning algorithm is proposed to learn the optimal admissible control policy using the data of the system states and inputs without requiring any knowledge of the system matrices. It is proven that the learning algorithm converges to the optimal admissible control policy. The implementation of the model-free algorithm is based on batch least squares and numerical average. The proposed algorithm is illustrated through a numerical example, which shows our algorithm outperforms other policy iteration algorithms.