Provably Efficient Representation Selection in Low-rank Markov Decision Processes: From Online to Offline RL
This work addresses the problem of efficient representation learning for researchers and practitioners in reinforcement learning, offering provable gains in both online and offline settings, though it is incremental as it builds on existing low-rank MDP frameworks.
The paper tackles representation selection in low-rank Markov Decision Processes for reinforcement learning, proposing the ReLEX algorithm with online and offline versions; results show that ReLEX-UCB achieves constant regret improvements under coverage conditions, and ReLEX-LCB attains constant sample complexity for optimal policy learning in offline RL, marking the first such result.
The success of deep reinforcement learning (DRL) lies in its ability to learn a representation that is well-suited for the exploration and exploitation task. To understand how the choice of representation can improve the efficiency of reinforcement learning (RL), we study representation selection for a class of low-rank Markov Decision Processes (MDPs) where the transition kernel can be represented in a bilinear form. We propose an efficient algorithm, called ReLEX, for representation learning in both online and offline RL. Specifically, we show that the online version of ReLEX, called ReLEX-UCB, always performs no worse than the state-of-the-art algorithm without representation selection, and achieves a strictly better constant regret if the representation function class has a "coverage" property over the entire state-action space. For the offline counterpart, ReLEX-LCB, we show that the algorithm can find the optimal policy if the representation class can cover the state-action space and achieves gap-dependent sample complexity. This is the first result with constant sample complexity for representation learning in offline RL.