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# Approximate Policy Iteration Schemes: A Comparison

*Proceedings of the 31st International Conference on Machine Learning*, PMLR 32(2):1314-1322, 2014.

#### Abstract

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_∞), 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(α), but this comes at the cost of a relative—exponential in \frac1ε—increase of the number of iterations. 2) PSDP_∞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_∞is proportional to their number of iterations, which may be problematic when the discount factor γis close to 1 or the approximation error εis 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.