Near-Optimal Primal-Dual Algorithm for Learning Linear Mixture CMDPs with Adversarial Rewards
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The paper introduces a new primal–dual algorithm for episodic adversarial linear constrained Markov decision processes (CMDPs) with unknown transitions. It achieves a rate‑optimal ×O(√K) regret and cumulative constraint violation, improving upon the previous ×O(K^{3/4}) bound and eliminating the need for Slater’s condition. The method combines adaptive FTRL, contracted value estimation, and an exponential Lyapunov function, enabling uniform concentration over the value function class and computational efficiency independent of the state‑space size.
arXiv:2607. 28390v1 Announce Type: new Abstract: Constrained Markov Decision Processes (CMDPs) provide a natural framework for reinforcement learning in safety-critical applications, where agents maximize long-term reward while satisfying long-term constraints.
The paper presents a unified framework for regularization-based robust reinforcement learning by deriving upper bounds on the performance gap between nominal and worst-case policies. These bounds are expressed as a regularization objective plus a KL-divergence penalty, explaining why KL penalties enhance robustness. The authors reformulate robust training as a constrained optimization problem, updating the Lagrange multiplier jointly with the policy to automatically tune regularization, and validate the approach with extensive adversarial evaluations on continuous control tasks.
arXiv:2509. 20114v3 Announce Type: replace Abstract: We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints.
arXiv:2606. 31480v1 Announce Type: new Abstract: We study constrained online convex optimization with adversarial losses and stochastic or adversarial constraints.
arXiv:2602. 01903v2 Announce Type: replace Abstract: This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime.