Inverse reinforcement learning (IRL) aims to recover the reward function of an expert agent from demonstrations of behavior. It is well known that the IRL problem is fundamentally ill-posed, i.e., many reward functions can explain the demonstrations. For this reason, IRL has been recently reframed in terms of estimating the feasible reward set, thus, postponing the selection of a single reward. However, so far, the available formulations and algorithmic solutions have been proposed and analyzed mainly for the online setting, where the learner can interact with the environment and query the expert at will. This is clearly unrealistic in most practical applications, where the availability of an offline dataset is a much more common scenario. In this paper, we introduce a novel notion of feasible reward set capturing the opportunities and limitations of the offline setting and we analyze the complexity of its estimation. This requires the introduction an original learning framework that copes with the intrinsic difficulty of the setting, for which the data coverage is not under control. Then, we propose two computationally and statistically efficient algorithms, IRLO and PIRLO, for addressing the problem. In particular, the latter adopts a specific form of pessimism to enforce the novel desirable property of inclusion monotonicity of the delivered feasible set. With this work, we aim to provide a panorama of the challenges of the offline IRL problem and how they can be fruitfully addressed.

逆强化学习（IRL）的目标是从行为示范中恢复专家智能体的奖励函数。本文介绍了一种新的可行奖励集概念，捕捉了离线设置的机会和限制，并分析了其估计的复杂性。通过引入针对该设置固有困难的原始学习框架，我们提出了两种计算和统计高效的算法，IRLO和PIRLO，用于解决这个问题。

离线逆强化学习：新的解决方案概念和可证明高效算法