In this paper, we investigate the problem of offline reinforcement learning with human feedback where feedback is available in the form of preference between trajectory pairs rather than explicit rewards. Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE. We consider the general reward setting where the reward can be defined over the whole trajectory and provide a novel guarantee that allows us to learn any target policy with a polynomial number of samples, as long as the target policy is covered by the offline data. This guarantee is the first of its kind with general function approximation. To measure the coverage of the target policy, we introduce a new single-policy concentrability coefficient, which can be upper bounded by the per-trajectory concentrability coefficient. We also establish lower bounds that highlight the necessity of such concentrability and the difference from standard RL, where state-action-wise rewards are directly observed. We further extend and analyze our algorithm when the feedback is given over action pairs.

翻译：本文研究基于人类偏好的离线强化学习问题，其中反馈以轨迹对偏好形式呈现，而非显式奖励。所提算法包含两个主要步骤：（1）利用离线数据通过最大似然估计（MLE）结合通用函数逼近估计隐式奖励；（2）在MLE置信集上求解分布鲁棒规划问题。我们考虑奖励可定义于整条轨迹的通用奖励设置，并给出新颖的理论保证：只要目标策略被离线数据覆盖，即可通过多项式级样本量学习任意目标策略。该保证是通用函数逼近框架下的首个同类结果。为度量目标策略的覆盖程度，我们引入新的单策略集中性系数，该系数可被逐轨迹集中性系数上界约束。我们还建立了下界，凸显此类集中性的必要性及与可观测状态-动作奖励的标准强化学习的本质差异。当反馈以动作对形式提供时，我们进一步扩展并分析了算法。