MFRLC：低秩约束马尔可夫决策过程的无模型表征学习算法
Provably Efficient Representation Learning for Low-Rank CMDPs
强化学习理论党看过来：MFRLC用LSVI-UCB加原始-对偶做约束MDP，拿到K^{3/4}次线性遗憾界，还不用估计转移核。
一篇arXiv论文研究低秩约束马尔可夫决策过程（CMDP）中的表征学习，提出无模型算法MFRLC。该算法结合LSVI-UCB与原始-对偶（primal-dual）技术，直接学习从表征到价值函数的映射，避免显式估计转移核。论文证明MFRLC在K轮部署中实现Õ(K^{3/4})的奖励遗憾与累计约束违反界，且与状态空间大小无关。据作者称，这是首个针对未知特征CMDP的次线性遗憾与违反保证。
Provably Efficient Representation Learning for Low-Rank CMDPs
We study representation learning in low-rank Constrained Markov Decision Processes (CMDPs), where both value and reward functions are approximated by a set of unknown representation vectors, and the transition dynamics admit a low-rank factorization. The objective is to maximize expected cumulative rewards while complying with constraints on the expected cumulative utility. To achieve this, we propose \texttt{MFRLC} (Model-Free Representation Learning for Low-Rank CMDP), a model-free algorithm that uses a primal-dual scheme to effectively balance reward regret and constraint violations. To the best of our knowledge, \texttt{MFRLC} is the first representation-learning method for low-rank CMDPs that combines the Least-Squares Value Iteration with Upper Confidence Bound (LSVI-UCB) and primal-dual techniques. \texttt{MFRLC} further enhances value function estimation with bonuses for function approximation and learns the mapping from representations to value functions directly, avoiding explicit estimation of the transition kernel. We prove that, with high probability, \texttt{MFRLC} achieves $\widetilde O(K^{3/4})$ reward regret and cumulative constraint violation over $K$ deployment rounds, independent of the size of the state space. To our knowledge, these are the first sublinear regret and violation guarantees for CMDPs with unknown features.