In this paper we consider the problem of learning an $\epsilon$-optimal policy for a discounted Markov Decision Process (MDP). Given an MDP with $S$ states, $A$ actions, the discount factor $\gamma \in (0,1)$, and an approximation threshold $\epsilon > 0$, we provide a model-free algorithm to learn an $\epsilon$-optimal policy with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{\epsilon^2(1-\gamma)^{5.5}})$ (where the notation $\tilde{O}(\cdot)$ hides poly-logarithmic factors of $S,A,1/(1-\gamma)$, and $1/\epsilon$) and success probability $(1-p)$. For small enough $\epsilon$, we show an improved algorithm with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{\epsilon^2(1-\gamma)^{3}})$. While the first bound improves upon all known model-free algorithms and model-based ones with tight dependence on $S$, our second algorithm beats all known sample complexity bounds and matches the information theoretic lower bound up to logarithmic factors.

本文提出了一种无模型的算法来学习具有折扣因子的马尔可夫决策过程中的政策，该算法的成功概率为(1-p)，且具有样本复杂度O(SALn(1/p)/(ε^2(1-γ)^3))，其中S是状态数，A是行动数，γ是折扣因子，ε是一个近似阈值

无模型强化学习：从剪切伪懊恼到样本复杂度