We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex problems we show that the PMD methods exhibit fast linear rate of convergence to the global optimality. We develop stochastic counterparts of these methods, and establish an ${\cal O}(1/\epsilon)$ (resp., ${\cal O}(1/\epsilon^2)$) sampling complexity for solving these RL problems with strongly (resp., general) convex regularizers using different sampling schemes, where $\epsilon$ denote the target accuracy. We further show that the complexity for computing the gradients of these regularizers, if necessary, can be bounded by ${\cal O}\{(\log_\gamma \epsilon) [(1-\gamma)L/\mu]^{1/2}\log (1/\epsilon)\}$ (resp., ${\cal O} \{(\log_\gamma \epsilon ) (L/\epsilon)^{1/2}\}$)for problems with strongly (resp., general) convex regularizers. Here $\gamma$ denotes the discounting factor. To the best of our knowledge, these complexity bounds, along with our algorithmic developments, appear to be new in both optimization and RL literature. The introduction of these convex regularizers also greatly expands the flexibility and applicability of RL models.

翻译：我们通过探讨这些总体高度非混凝土问题的结构特性,我们展示了这些总体高度非混凝土问题的结构特性。我们开发了这些方法的随机对应方法(1/\epsilon),并建立了美元O}(1-\gamma)美元(resp.)1/2美元(1/\epsilon2美元),为解决这些强化学习(RL)问题而抽样复杂程度,用不同的取样方法(resp.,一般)解决这些RL问题。我们进一步表明,如果有必要,计算这些规范者梯度的复杂程度可以受美元O ⁇ (log ⁇ ma) (1/\gamma)美元([1-\gamma)L/\mu] 美元(1/2 ⁇ log (1/\\ epsilon) 美元(respreplicalityrs) 和这些常价Lislus 的精度(xalislationalislationalislation) 。