A. Aniket and A. Chattopadhyay, Online Reinforcement Learning in Periodic MDP, IEEE Transactions on Artificial Intelligence, vol. 5, no. 7, pp. 3624-3637, July 2024 DOI: 10.1109/TAI.2024.3375258.
We study learning in periodic Markov decision process (MDP), a special type of nonstationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period N and as O(TlogT−−−−−√) with the horizon length T . Utilizing the information about the sparsity of transition matrix of augmented MDP, we propose another algorithm [periodic upper confidence reinforcement learning with Bernstein bounds (PUCRLB) which enhances upon PUCRL2, both in terms of regret ( O(N−−√) dependency on period] and empirical performance. Finally, we propose two other algorithms U-PUCRL2 and U-PUCRLB for extended uncertainty in the environment in which the period is unknown but a set of candidate periods are known. Numerical results demonstrate the efficacy of all the algorithms.