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

Publication ,  Conference
Naeem, MA; Pajic, M
Published in: Proceedings of Machine Learning Research
January 1, 2023

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 (i.e., rewards), while neither assuming reversibility nor exact knowledge of the considered random dynamical system (assumptions at heart of concentration inequalities in statistical mechanics and Markov diffusion processes).

Duke Scholars

Published In

Proceedings of Machine Learning Research

EISSN

2640-3498

Publication Date

January 1, 2023

Volume

211

Start / End Page

653 / 664
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Naeem, M. A., & Pajic, M. (2023). Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space. In Proceedings of Machine Learning Research (Vol. 211, pp. 653–664).
Naeem, M. A., and M. Pajic. “Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space.” In Proceedings of Machine Learning Research, 211:653–64, 2023.
Naeem MA, Pajic M. Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space. In: Proceedings of Machine Learning Research. 2023. p. 653–64.
Naeem, M. A., and M. Pajic. “Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space.” Proceedings of Machine Learning Research, vol. 211, 2023, pp. 653–64.
Naeem MA, Pajic M. Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space. Proceedings of Machine Learning Research. 2023. p. 653–664.

Published In

Proceedings of Machine Learning Research

EISSN

2640-3498

Publication Date

January 1, 2023

Volume

211

Start / End Page

653 / 664