Square-root regret bounds for continuous-time episodic Markov decision processes
This work addresses the problem of efficient learning in continuous-time MDPs for researchers and practitioners in reinforcement learning, representing an incremental advance by extending regret analysis to this setting.
The authors tackled reinforcement learning for continuous-time Markov decision processes (MDPs) in the episodic setting by developing an algorithm based on value iteration and upper confidence bounds, achieving worst-case expected regret bounds of order square-root on the number of episodes, with simulation experiments illustrating its performance.
We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the inter-transition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state--action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst-case expected regret for the proposed algorithm, and establish a worst-case lower bound, both bounds are of the order of square-root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.