The paper addresses the challenge of representation transfer in offline Reinforcement Learning (RL) for low-rank Markov Decision Processes (MDPs). The authors propose an algorithm that learns a shared representation from multiple source tasks and uses it to plan a near-optimal policy for a target task. Unlike online RL, where the agent interacts with the environment during learning, offline RL cannot interact with the environment, leading to potential incomplete coverage of the state-action space. The key contributions include: 1. **Pointwise Uncertainty Measures**: The algorithm computes pointwise uncertainty measures for the learned representation, addressing the challenge of non-linear function approximation in low-rank MDPs. 2. **Effective Occupancy Density**: Inspired by non-parametric estimation, the algorithm introduces the concept of effective occupancy density to capture the coverage of state-action pairs across all source datasets. 3. **Theoretical Analysis**: The paper provides a data-dependent upper bound on the suboptimality of the learned policy for the target task, highlighting three key factors: source task coverage of the target task's optimal policy, source task coverage of offline samples from the target task, and target task coverage of its optimal policy. 4. **Empirical Validation**: The algorithm is empirically validated on a rich-observation MDP, demonstrating its effectiveness in leveraging historical data from multiple source tasks for few-shot learning on the target task. The paper also discusses the limitations of existing offline RL algorithms and shows that their performance can be suboptimal without penalizing the representation transfer. The proposed algorithm, Pessimistic RepTransfer (PRT), is shown to outperform baselines in scenarios with less explored source datasets, emphasizing the importance of uncertainty quantification in the learned representation.The paper addresses the challenge of representation transfer in offline Reinforcement Learning (RL) for low-rank Markov Decision Processes (MDPs). The authors propose an algorithm that learns a shared representation from multiple source tasks and uses it to plan a near-optimal policy for a target task. Unlike online RL, where the agent interacts with the environment during learning, offline RL cannot interact with the environment, leading to potential incomplete coverage of the state-action space. The key contributions include: 1. **Pointwise Uncertainty Measures**: The algorithm computes pointwise uncertainty measures for the learned representation, addressing the challenge of non-linear function approximation in low-rank MDPs. 2. **Effective Occupancy Density**: Inspired by non-parametric estimation, the algorithm introduces the concept of effective occupancy density to capture the coverage of state-action pairs across all source datasets. 3. **Theoretical Analysis**: The paper provides a data-dependent upper bound on the suboptimality of the learned policy for the target task, highlighting three key factors: source task coverage of the target task's optimal policy, source task coverage of offline samples from the target task, and target task coverage of its optimal policy. 4. **Empirical Validation**: The algorithm is empirically validated on a rich-observation MDP, demonstrating its effectiveness in leveraging historical data from multiple source tasks for few-shot learning on the target task. The paper also discusses the limitations of existing offline RL algorithms and shows that their performance can be suboptimal without penalizing the representation transfer. The proposed algorithm, Pessimistic RepTransfer (PRT), is shown to outperform baselines in scenarios with less explored source datasets, emphasizing the importance of uncertainty quantification in the learned representation.