论文标题
大规模马尔可夫决策过程的不精确的GMRES政策迭代
Inexact GMRES Policy Iteration for Large-Scale Markov Decision Processes
论文作者
论文摘要
政策迭代享有局部二次收缩率，但其迭代量对于马尔可夫决策过程（MDP）在计算上昂贵。鉴于政策迭代与半齿牛顿方法之间的联系并从后者的不精确变体中汲取灵感，我们提出了\ textit {Intecact Policy Iteration}，这是一种新的有限MDP的方法，具有局部收缩保证。然后，我们根据GMRE部署进行近似政策评估步骤设计一个实例，我们称之为不精确的GMRES策略迭代。最后，我们在具有10000个州的MDP上证明了不精确的GMRES政策迭代的出色实践绩效，该迭代分别在政策迭代和乐观的政策迭代方面达到了$ \ times 5.8 $和$ \ times 2.2 $速度。
Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the semismooth Newton method and taking inspiration from the inexact variants of the latter, we propose \textit{inexact policy iteration}, a new class of methods for large-scale finite MDPs with local contraction guarantees. We then design an instance based on the deployment of GMRES for the approximate policy evaluation step, which we call inexact GMRES policy iteration. Finally, we demonstrate the superior practical performance of inexact GMRES policy iteration on an MDP with 10000 states, where it achieves a $\times 5.8$ and $\times 2.2$ speedup with respect to policy iteration and optimistic policy iteration, respectively.
