Provably Efficient Offline Reinforcement Learning With Trajectory-Wise Reward

The remarkable success of reinforcement learning (RL) heavily relies on observing the reward of every visited state-action pair. In many real world applications, however, an agent can observe only a score that represents the quality of the whole trajectory, which is referred to as the trajectory-wise reward. In such a situation, it is difficult for standard RL methods to well utilize trajectory-wise reward, and large bias and variance errors can be incurred in policy evaluation. In this work, we propose a novel offline RL algorithm, called Pessimistic vAlue iteRaTion with rEward Decomposition (PARTED), which decomposes the trajectory return into per-step proxy rewards via least-squares-based reward redistribution, and then performs pessimistic value iteration based on the learned proxy reward. To ensure the value functions constructed by PARTED are always pessimistic with respect to the optimal ones, we design a new penalty term to offset the uncertainty of the proxy reward. We first show that our PARTED achieves an
$\tilde {\mathcal {O}}(dH^{3}/\sqrt {N})$
suboptimality for linear MDPs, where d is the dimension of the feature, H is the episode length, and N is the size of the offline dataset. We further extend our algorithm and results to general large-scale episodic MDPs with neural network function approximation. To the best of our knowledge, PARTED is the first offline RL algorithm that is provably efficient in general MDP with trajectory-wise reward.