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 {\em 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. For general episodic MDPs with large state space, we show that PARTED with overparameterized neural network function approximation achieves an $\tilde{\mathcal{O}}(D_{\text{eff}}H^2/\sqrt{N})$ suboptimality, where $H$ is the length of episode, $N$ is the total number of samples, and $D_{\text{eff}}$ is the effective dimension of the neural tangent kernel matrix. To further illustrate the result, we show that PARTED achieves an $\tilde{\mathcal{O}}(dH^3/\sqrt{N})$ suboptimality with linear MDPs, where $d$ is the feature dimension, which matches with that with neural network function approximation, when $D_{\text{eff}}=dH$. To the best of our knowledge, PARTED is the first offline RL algorithm that is provably efficient in general MDP with trajectory-wise reward.

本文提出了一种新颖的离线 RL 算法，PARTED，可将轨迹回报分解为逐步代理奖励，具有一定的收敛上界，该算法可以有效地处理观察到的轨迹奖励问题。

轨迹-wise 奖励的可证明高效离线强化学习