Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space
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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).
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 8 of its 25 references that are in the map. First posted on arXiv 25 May 2022.
Builds on
8 of 25 references.
References · 8
- 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
- 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
- 2021On-Policy Deep Reinforcement Learning for the Average-Reward Criterioncited by 29
- 2017Least-Squares Temporal Difference Learning for the Linear Quadratic Regulatorcited by 27
- 2018Stochastic Gradient Descent Learns State Equations with Nonlinear Activationscited by 16
- 2020Adaptive Approximate Policy Iterationcited by 9
- 2019Unknown mixing times in apprenticeship and reinforcement learningcited by 7
- 2020Learning Expected Reward for Switched Linear Control Systems: A Non-Asymptotic Viewcited by 1
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Citing papers per year: 2022: 1; 2023: 1.
2 papers.