arXiv AI
Windowed A-K-MDP
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The paper introduces REP-PD-TEG, a representation‑learning algorithm for low‑rank continuous‑state constrained Markov Decision Processes (CMDPs) that achieves optimal ≥O(√K) regret in the soft cumulative‑violation setting while maintaining a ≥O(K^{3/4}) sample bound when exploratory actions are penalised. For the stricter hard cumulative‑violation scenario, REP-PD-H-TEG is proposed, which uses a bonus‑corrected lower‑confidence utility certificate and a stabilized dual search to guarantee both regret and hard‑violation bounds. Together, these methods provide the first theoretically guaranteed representation‑learning framework for low‑rank continuous‑state CMDPs with both soft and hard violation controls.