We consider discounted infinite horizon constrained Markov decision processes (CMDPs) where the goal is to find an optimal policy that maximizes the expected cumulative reward subject to expected cumulative constraints. Motivated by the application of CMDPs in online learning of safety-critical systems, we focus on developing an algorithm that ensures constraint satisfaction during learning. To this end, we develop a zeroth-order interior point approach based on the log barrier function of the CMDP. Under the commonly assumed conditions of Fisher non-degeneracy and bounded transfer error of the policy parameterization, we establish the theoretical properties of the algorithm. In particular, in contrast to existing CMDP approaches that ensure policy feasibility only upon convergence, our algorithm guarantees feasibility of the policies during the learning process and converges to the optimal policy with a sample complexity of $O(\varepsilon^{-6})$. In comparison to the state-of-the-art policy gradient-based algorithm, C-NPG-PDA, our algorithm requires an additional $O(\varepsilon^{-2})$ samples to ensure policy feasibility during learning with same Fisher-non-degenerate parameterization.

在无限时间、约束的马尔科夫决策过程中，通过零阶内点方法实现约束满足，以最大化预期累积奖励，确保策略在学习过程中的可行性，并具有样本复杂度O(ε^(-6))

具有全局收敛保证的内点约束强化学习