论文标题
在连续状态空间上进行动力系统的运输 - 质量，Lyapunov稳定性和采样
Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space
论文作者
论文摘要
我们研究具有无限状态空间的离散时间随机动力系统的浓度现象。我们开发了一种使用完全功能分析框架为动态系统获得指数浓度不平等的启发式方法。我们还表明，与纯粹的确定性设置相比，指数型lyapunov函数的存在不仅意味着稳定性，而且还意味着通过\ emph {transport-entrypropy nodebality}（t-e）（t-e）通过固定分布采样的指数浓度不平等。这些结果在\ emph {强化学习}（RL）和\ emph {对照}中具有重大影响，即使对于无限制的可观察力，也会导致指数浓度的不平等，同时既没有假设对随机动力学系统的可逆性知识，也不是对随机动力学系统的精确知识（统计机械师和Markov扩散过程中浓度达到浓度的假设）。
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 \emph{transport-entropy inequality} (T-E). These results have significant impact in \emph{reinforcement learning} (RL) and \emph{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).
