Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety constraints. The problem is mathematically formulated as constrained Markov decision process (CMDP). In the literature, various algorithms are available to solve CMDP problems in a model-free manner to achieve $\epsilon$-optimal cumulative reward with $\epsilon$ feasible policies. An $\epsilon$-feasible policy implies that it suffers from constraint violation. An important question here is whether we can achieve $\epsilon$-optimal cumulative reward with zero constraint violations or not. To achieve that, we advocate the use of a randomized primal-dual approach to solving the CMDP problems and propose a conservative stochastic primal-dual algorithm (CSPDA) which is shown to exhibit $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity to achieve $\epsilon$-optimal cumulative reward with zero constraint violations. In the prior works, the best available sample complexity for the $\epsilon$-optimal policy with zero constraint violation is $\tilde{\mathcal{O}}(1/\epsilon^5)$. Hence, the proposed algorithm provides a significant improvement as compared to the state of the art.

该研究提出了一种保守随机原始-对偶算法(CSPDA)，用于解决基于约束马尔可夫决策过程(CMDP)的强化学习问题，该算法能够在零约束违规的情况下实现ε-最优累积奖励，并提供比现有算法更有效率的复杂度。

通过原始对偶方法实现有约束强化学习的零约束违规