Provable Multi-Task Reinforcement Learning: A Representation Learning Framework with Low Rank Rewards
arXiv:2604.03891v1 Announce Type: new Abstract: Multi-task representation learning (MTRL) is an approach that learns shared latent representations across related tasks, facilitating collaborative learning that improves the overall learning efficiency. This paper studies MTRL for multi-task reinforcement learning (RL), where multiple tasks have the same state-action space and transition probabilities, but different rewards. We consider T linear Markov Decision Processes (MDPs) where the reward functions and transition dynamics admit linear feature embeddings of dimension d. The relatedness among the tasks is captured by a low-rank structure on the reward matrices. Learning shared representations across multiple RL tasks is challenging due to the complex and policy-dependent nature of data that leads to a temporal progression of error. Our approach adopts a reward-free reinforcement learning framework to first learn a data-collection policy. This policy then informs an exploration strat
arXiv:2604.03891v1 Announce Type: new Abstract: Multi-task representation learning (MTRL) is an approach that learns shared latent representations across related tasks, facilitating collaborative learning that improves the overall learning efficiency. This paper studies MTRL for multi-task reinforcement learning (RL), where multiple tasks have the same state-action space and transition probabilities, but different rewards. We consider T linear Markov Decision Processes (MDPs) where the reward functions and transition dynamics admit linear feature embeddings of dimension d. The relatedness among the tasks is captured by a low-rank structure on the reward matrices. Learning shared representations across multiple RL tasks is challenging due to the complex and policy-dependent nature of data that leads to a temporal progression of error. Our approach adopts a reward-free reinforcement learning framework to first learn a data-collection policy. This policy then informs an exploration strategy for estimating the unknown reward matrices. Importantly, the data collected under this well-designed policy enable accurate estimation, which ultimately supports the learning of an near-optimal policy. Unlike existing approaches that rely on restrictive assumptions such as Gaussian features, incoherence conditions, or access to optimal solutions, we propose a low-rank matrix estimation method that operates under more general feature distributions encountered in RL settings. Theoretical analysis establishes that accurate low-rank matrix recovery is achievable under these relaxed assumptions, and we characterize the relationship between representation error and sample complexity. Leveraging the learned representation, we construct near-optimal policies and prove a regret bound. Experimental results demonstrate that our method effectively learns robust shared representations and task dynamics from finite data.
Executive Summary
This paper proposes a novel framework for multi-task reinforcement learning (MTRL) that learns shared latent representations across related tasks. The approach, called Provable Multi-Task Reinforcement Learning, leverages a low-rank structure on reward matrices and a data-collection policy to estimate unknown reward functions. Theoretical analysis shows that accurate low-rank matrix recovery is achievable under general feature distributions, and experimental results demonstrate the method's effectiveness in learning robust shared representations and task dynamics. The paper's contributions include a low-rank matrix estimation method and a representation learning framework that operates under relaxed assumptions. The approach has implications for improving learning efficiency and reducing sample complexity in MTRL. However, the method's performance may degrade in settings with high-dimensional state-action spaces or complex task relationships.
Key Points
- ▸ Proposes a novel framework for multi-task reinforcement learning (MTRL) that learns shared latent representations across related tasks
- ▸ Leverages a low-rank structure on reward matrices and a data-collection policy to estimate unknown reward functions
- ▸ Theoretical analysis shows that accurate low-rank matrix recovery is achievable under general feature distributions
Merits
Strength in Relaxing Assumptions
The proposed method operates under more general feature distributions encountered in RL settings, relaxing the restrictive assumptions found in existing approaches.
Effective Estimation of Reward Matrices
The data-collection policy enables accurate estimation of unknown reward matrices, which is critical for learning shared representations and near-optimal policies.
Robust Shared Representations and Task Dynamics
Experimental results demonstrate that the method effectively learns robust shared representations and task dynamics from finite data.
Demerits
Limitation in High-Dimensional State-Action Spaces
The method's performance may degrade in settings with high-dimensional state-action spaces or complex task relationships.
Potential Overfitting to Specific Data
The reliance on a data-collection policy may lead to overfitting to specific data, which could limit the method's generalizability.
Expert Commentary
The proposed framework for multi-task reinforcement learning is a significant contribution to the field, as it offers a more general and scalable approach to learning shared representations across related tasks. The method's ability to operate under relaxed assumptions and its effectiveness in estimating unknown reward matrices make it an attractive solution for real-world applications. However, further research is needed to address the limitations and potential pitfalls of the approach. Specifically, the method's performance in high-dimensional state-action spaces and its susceptibility to overfitting require careful consideration. Additionally, the proposed method's relationship to existing approaches to deep multi-task learning and transfer learning should be further explored to provide a more comprehensive understanding of its implications and applications.
Recommendations
- ✓ Further research is needed to address the limitations and potential pitfalls of the proposed method, particularly in high-dimensional state-action spaces and its susceptibility to overfitting.
- ✓ The proposed method should be compared to existing approaches to deep multi-task learning and transfer learning to provide a more comprehensive understanding of its implications and applications.
Sources
Original: arXiv - cs.LG