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 ϵ1-- 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