arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1909.09186cs.LGcs.AI
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再论矩阵形式的策略优化

Revisit Policy Optimization in Matrix Form

McGill University(麦吉尔大学);Mila(米拉);DeepMind(深度思维)

Sitao Luan, Xiao-Wen Chang, Doina Precup

摘要:

在表格的情况下,当奖励和环境动态是已知的时,策略评估可以写为$\bm{V}_{\bmπ} = (I - γP_{\bmπ})^{-1} \bm{r}_{\bmπ}$,其中$P_{\bmπ}$是给定策略${\bmπ}$的状态转移矩阵,而$\bm{r}_{\bmπ}$是给定${\bmπ}$的奖励信号。令我们烦恼的是,$P_{\bmπ}$和$\bm{r}_{\bmπ}$都与${\bmπ}$混在一起,这意味着每次我们更新${\bmπ}$时,它们都会一起改变。在本文中,我们利用符号从\cite{wang2007dual}解开${\bmπ}$和环境动态,使优化策略更直接。我们表明,策略梯度定理\cite{sutton2018reinforcement}和TRPO \cite{schulman2015trust}可以放在一个更一般的框架,这样的符号有很好的潜力,可以扩展到基于模型的强化学习。

英文摘要:

In tabular case, when the reward and environment dynamics are known, policy evaluation can be written as $\bm{V}_{\bmπ} = (I - γP_{\bmπ})^{-1} \bm{r}_{\bmπ}$, where $P_{\bmπ}$ is the state transition matrix given policy ${\bmπ}$ and $\bm{r}_{\bmπ}$ is the reward signal given ${\bmπ}$. What annoys us is that $P_{\bmπ}$ and $\bm{r}_{\bmπ}$ are both mixed with ${\bmπ}$, which means every time when we update ${\bmπ}$, they will change together. In this paper, we leverage the notation from \cite{wang2007dual} to disentangle ${\bmπ}$ and environment dynamics which makes optimization over policy more straightforward. We show that policy gradient theorem \cite{sutton2018reinforcement} and TRPO \cite{schulman2015trust} can be put into a more general framework and such notation has good potential to be extended to model-based reinforcement learning.

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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