Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework.

提出了一种用于非线性函数逼近的离线强化学习方法——悲观非线性最小二乘值迭代(PNLSVI)，它包括方差加权回归、方差估计子程序和基于悲观值迭代的规划阶段。该方法的遗憾界与函数类的复杂性紧密相关，并在针对线性函数逼近的情况下实现极小化的最优实例相关遗憾。在前期研究基础上，扩展到更一般的框架。

脱机强化学习的悲观非线性最小二乘值迭代