arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.04353cs.LGstat.ML
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无界状态空间下的稳定强化学习

Stable Reinforcement Learning with Unbounded State Space

MIT(麻省理工学院);Cornell University(康奈尔大学)

Devavrat Shah, Qiaomin Xie, Zhi Xu

摘要:

本文考虑了由调度网络中的经典调度问题所激发的具有无界状态空间的强化学习(RL)问题。传统的策略以及为有限、有界或紧凑状态空间设计的误差度量需要无限样本来为无界状态空间提供任何有意义的性能保证(例如,$\ell_\infty$误差)。也就是说,我们需要一个新的性能度量概念。作为这项工作的主要贡献,在排队系统与控制理论的文献的启发下,我们提出了稳定性的概念“善良”的状态动态下的政策应保持在一个有界区域的高概率。作为概念的证明,我们提出了一个RL政策,使用稀疏采样为基础的Monte Carlo Oracle,并认为它满足稳定性,只要系统动力学下的最优策略尊重李雅普诺夫函数。存在李雅普诺夫函数的假设不是限制性的,因为它等价于任何马尔可夫链的正递归或稳定性,即,如果有任何政策可以稳定系统,那么它必须拥有一个李雅普诺夫函数。而且,我们的政策不利用知识的具体李雅普诺夫函数。为了使我们的方法样本效率,我们提供了一个改进的,样本效率的稀疏采样的蒙特卡罗Oracle与Lipschitz价值函数,可能是在自己的权利感兴趣。此外,我们设计了一个自适应版本的算法,精心构造的统计测试,自动找到正确的调整参数的基础上。

英文摘要:

We consider the problem of reinforcement learning (RL) with unbounded state space motivated by the classical problem of scheduling in a queueing network. Traditional policies as well as error metric that are designed for finite, bounded or compact state space, require infinite samples for providing any meaningful performance guarantee (e.g. $\ell_\infty$ error) for unbounded state space. That is, we need a new notion of performance metric. As the main contribution of this work, inspired by the literature in queuing systems and control theory, we propose stability as the notion of "goodness": the state dynamics under the policy should remain in a bounded region with high probability. As a proof of concept, we propose an RL policy using Sparse-Sampling-based Monte Carlo Oracle and argue that it satisfies the stability property as long as the system dynamics under the optimal policy respects a Lyapunov function. The assumption of existence of a Lyapunov function is not restrictive as it is equivalent to the positive recurrence or stability property of any Markov chain, i.e., if there is any policy that can stabilize the system then it must possess a Lyapunov function. And, our policy does not utilize the knowledge of the specific Lyapunov function. To make our method sample efficient, we provide an improved, sample efficient Sparse-Sampling-based Monte Carlo Oracle with Lipschitz value function that may be of interest in its own right. Furthermore, we design an adaptive version of the algorithm, based on carefully constructed statistical tests, which finds the correct tuning parameter automatically.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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