Provably Efficient Reinforcement Learning in Continuous-Time Episodic MDPs with Poisson Decision Epochs

Abstract:Many real-world reinforcement learning (RL) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time Markov Decision Processes (MDPs) in which decision epochs are governed by a homogeneous Poisson process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of Poisson decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL (Auer and Ortner 2006) and Q-learning (Jin et al. 2018) to this setting, proving $\widetilde{O}(T^{2/3})$ regret bounds for both model-based and model-free algorithms. Finally, we establish matching $\widetilde{\Omega}(T^{2/3})$ minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic MDPs with Poisson decision epochs.

Machine Learning (cs.LG)

arXiv:2609.23127 [cs.LG]

(or arXiv:2609.23127v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.23127 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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