Xuefeng Gao

Xuefeng Gao, Xun Yu Zhou

We consider reinforcement learning for continuous-time Markov decision processes (MDPs) in the infinite-horizon, average-reward setting. In contrast to discrete-time MDPs, a continuous-time process moves to a state and stays there for a random holding time after an action is taken. With unknown transition probabilities and rates of exponential holding times, we derive instance-dependent regret lower bounds that are logarithmic in the time horizon. Moreover, we design a learning algorithm and establish a finite-time regret bound that achieves the logarithmic growth rate. Our analysis builds upon upper confidence reinforcement learning, a delicate estimation of the mean holding times, and stochastic comparison of point processes.

Xuefeng Gao, Xun Yu Zhou

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.

Wenhao Xu, Xuefeng Gao, Xuedong He

The optimized certainty equivalent (OCE) is a family of risk measures that cover important examples such as entropic risk, conditional value-at-risk and mean-variance models. In this paper, we propose a new episodic risk-sensitive reinforcement learning formulation based on tabular Markov decision processes with recursive OCEs. We design an efficient learning algorithm for this problem based on value iteration and upper confidence bound. We derive an upper bound on the regret of the proposed algorithm, and also establish a minimax lower bound. Our bounds show that the regret rate achieved by our proposed algorithm has optimal dependence on the number of episodes and the number of actions.

Yi Xiong, Ningyuan Chen, Xuefeng Gao et al.

We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the average reward over an infinite horizon. We propose a learning algorithm for this problem, building on spectral method-of-moments estimations for hidden Markov models, the belief error control in POMDPs and upper-confidence-bound methods for online learning. We establish a regret bound of $O(T^{2/3}\sqrt{\log T})$ for the proposed learning algorithm where $T$ is the learning horizon. This is, to the best of our knowledge, the first algorithm achieving sublinear regret with respect to our oracle for learning general POMDPs.