Constrained Markov decision processes (CMDPs) model scenarios of sequential decision making with multiple objectives that are increasingly important in many applications. However, the model is often unknown and must be learned online while still ensuring the constraint is met, or at least the violation is bounded with time. Some recent papers have made progress on this very challenging problem but either need unsatisfactory assumptions such as knowledge of a safe policy, or have high cumulative regret. We propose the Safe PSRL (posterior sampling-based RL) algorithm that does not need such assumptions and yet performs very well, both in terms of theoretical regret bounds as well as empirically. The algorithm achieves an efficient tradeoff between exploration and exploitation by use of the posterior sampling principle, and provably suffers only bounded constraint violation by leveraging the idea of pessimism. Our approach is based on a primal-dual approach. We establish a sub-linear $\tilde{\mathcal{ O}}\left(H^{2.5} \sqrt{|\mathcal{S}|^2 |\mathcal{A}| K} \right)$ upper bound on the Bayesian reward objective regret along with a bounded, i.e., $\tilde{\mathcal{O}}\left(1\right)$ constraint violation regret over $K$ episodes for an $|\mathcal{S}|$-state, $|\mathcal{A}|$-action and horizon $H$ CMDP.

本研究提出了一种基于后验抽样的强化学习算法Safe PSRL，它能够在不需要安全策略的前提下有效地平衡探索和开发，并通过采用悲观主义的思想仅受到有界的约束违规，从而在理论和实践上得到了良好的表现。

受限MDP的安全后验采样与约束违规的界限控制