We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), a natural adaptation of the Policy Search by Dynamic Programming algorithm to the infinite-horizon case (PSDP$_\infty$), and the recently proposed Non-Stationary Policy iteration (NSPI(m)). For all algorithms, we describe performance bounds, and make a comparison by paying a particular attention to the concentrability constants involved, the number of iterations and the memory required. Our analysis highlights the following points: 1) The performance guarantee of CPI can be arbitrarily better than that of API/API($\alpha$), but this comes at the cost of a relative---exponential in $\frac{1}{\epsilon}$---increase of the number of iterations. 2) PSDP$_\infty$ enjoys the best of both worlds: its performance guarantee is similar to that of CPI, but within a number of iterations similar to that of API. 3) Contrary to API that requires a constant memory, the memory needed by CPI and PSDP$_\infty$ is proportional to their number of iterations, which may be problematic when the discount factor $\gamma$ is close to 1 or the approximation error $\epsilon$ is close to $0$; we show that the NSPI(m) algorithm allows to make an overall trade-off between memory and performance. Simulations with these schemes confirm our analysis.

本文考虑了马尔可夫决策过程所形式化的无限时间折扣率下的最优控制问题，研究了几种近似策略迭代算法，对它们进行了性能分析，显示了非静态策略迭代算法可以在内存和性能之间进行平衡。

近似策略迭代方案对比