# Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space

arXiv: https://arxiv.org/abs/2205.12448 · HTML: https://mlsanity.com/paper/2205.12448/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 8 of 8)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Least-Squares Temporal Difference Learning for the Linear Quadratic Regulator](https://mlsanity.com/paper/1712.08642/) (2017)
- [On-Policy Deep Reinforcement Learning for the Average-Reward Criterion](https://mlsanity.com/paper/2106.07329/) (2021)
- [Stochastic Gradient Descent Learns State Equations with Nonlinear Activations](https://mlsanity.com/paper/1809.03019/) (2018)
- [Adaptive Approximate Policy Iteration](https://mlsanity.com/paper/2002.03069/) (2020)
- [Unknown mixing times in apprenticeship and reinforcement learning](https://mlsanity.com/paper/1905.09704/) (2019)
- [Learning Expected Reward for Switched Linear Control Systems: A Non-Asymptotic View](https://mlsanity.com/paper/2006.08105/) (2020)

## Built on by (most cited first, 2 of 2)

- [Concentration Phenomenon for Random Dynamical Systems: An Operator Theoretic Approach](https://mlsanity.com/paper/2212.03670/) (2022)
- [Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approach](https://mlsanity.com/paper/2304.01708/) (2023)

## Abstract (arXiv)

We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely functional analytic framework. We also show that existence of exponential-type Lyapunov function, compared to the purely deterministic setting, not only implies stability but also exponential concentration inequalities for sampling from the stationary distribution, via transport-entropy inequality (T-E). These results have significant impact in reinforcement learning (RL) and controls, leading to exponential concentration inequalities even for unbounded observables, while neither assuming reversibility nor exact knowledge of random dynamical system (assumptions at heart of concentration inequalities in statistical mechanics and Markov diffusion processes).