We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI) scheme via an -approximate greedy operator (Kakade and Langford, 2002; Lazaric et al., 2010). We describe existing and a few new performance bounds for Direct Policy Iteration (DPI) (Lagoudakis and Parr, 2003; Fern et al., 2006; Lazaric et al., 2010) and Conservative Policy Iteration (CPI) (Kakade and Langford, 2002). By paying a particular attention to the concentrability constants involved in such guarantees, we notably argue that the guarantee of CPI is much better than that of DPI, but this comes at the cost of a relative--exponential in $\frac{1}{\epsilon}$-- increase of time complexity. We then describe an algorithm, Non-Stationary Direct Policy Iteration (NSDPI), that can either be seen as 1) a variation of Policy Search by Dynamic Programming by Bagnell et al. (2003) to the infinite horizon situation or 2) a simplified version of the Non-Stationary PI with growing period of Scherrer and Lesner (2012). We provide an analysis of this algorithm, that shows in particular that it enjoys the best of both worlds: its performance guarantee is similar to that of CPI, but within a time complexity similar to that of DPI.

本篇研究考虑了马尔科夫决策过程(Markov Decision Processes)的无限时间折扣优化控制问题，并提供了Policy Search算法以及Direct Policy Iteration和Conservative Policy Iteration的性能保证，同时提出了Non-Stationary Direct Policy Iteration算法，并证明其时间复杂度类似于DPI，性能保证好于DPI，且与CPI相当。

关于某些策略搜索动态规划算法的性能界限