arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.12956cs.LGstat.ML
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改进(自然)Actor-Critic算法的样本复杂度界

Improving Sample Complexity Bounds for (Natural) Actor-Critic Algorithms

The Ohio State University(俄亥俄州立大学)

Tengyu Xu, Zhe Wang, Yingbin Liang

摘要:

行动者-评论者(AC)算法是强化学习中寻找最优策略的常用方法。在无限水平的情况下,有限样本收敛速度的AC和自然演员批评(NAC)算法最近已经建立,但在独立同分布(i.i.d.)采样和单样本更新在每次迭代。相比之下,本文的特征的收敛速度和样本复杂性的AC和NAC下马尔可夫抽样,与小批量数据的每次迭代,并与演员具有一般的政策类近似。我们表明,一个小批量AC达到$ε$ -准确的平稳点的整体样本复杂性提高了最好的已知的样本复杂性AC的顺序$\mathcal{O}(ε^{-1}\log(1/ε))$,和整体样本复杂性的一个小批量NAC达到$ε$ -准确的全局最优点提高了现有的样本复杂性NAC的顺序$\mathcal{O}(ε^{-1}/\log(1/ε))$。此外,AC和NAC的样本复杂度的特点,在这项工作中优于策略梯度(PG)和自然的策略梯度(NPG)的$\mathcal{O}((1-γ)^{-3})$和$\mathcal{O}((1-γ)^{-4}ε^{-1}/\log(1/ε))$的一个因素,分别。这是第一个理论研究,建立AC和NAC实现有序性能改善PG和NPG无限地平线下,由于纳入批评。

英文摘要:

The actor-critic (AC) algorithm is a popular method to find an optimal policy in reinforcement learning. In the infinite horizon scenario, the finite-sample convergence rate for the AC and natural actor-critic (NAC) algorithms has been established recently, but under independent and identically distributed (i.i.d.) sampling and single-sample update at each iteration. In contrast, this paper characterizes the convergence rate and sample complexity of AC and NAC under Markovian sampling, with mini-batch data for each iteration, and with actor having general policy class approximation. We show that the overall sample complexity for a mini-batch AC to attain an $ε$-accurate stationary point improves the best known sample complexity of AC by an order of $\mathcal{O}(ε^{-1}\log(1/ε))$, and the overall sample complexity for a mini-batch NAC to attain an $ε$-accurate globally optimal point improves the existing sample complexity of NAC by an order of $\mathcal{O}(ε^{-1}/\log(1/ε))$. Moreover, the sample complexity of AC and NAC characterized in this work outperforms that of policy gradient (PG) and natural policy gradient (NPG) by a factor of $\mathcal{O}((1-γ)^{-3})$ and $\mathcal{O}((1-γ)^{-4}ε^{-1}/\log(1/ε))$, respectively. This is the first theoretical study establishing that AC and NAC attain orderwise performance improvement over PG and NPG under infinite horizon due to the incorporation of critic.

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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