Provable Multi-Task Reinforcement Learning: A Representation Learning Framework with Low Rank Rewards
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911567838183424 |
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| author | Guo, Yaoze Moothedath, Shana |
| author_facet | Guo, Yaoze Moothedath, Shana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03891 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Provable Multi-Task Reinforcement Learning: A Representation Learning Framework with Low Rank Rewards Guo, Yaoze Moothedath, Shana Machine Learning 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. |
| title | Provable Multi-Task Reinforcement Learning: A Representation Learning Framework with Low Rank Rewards |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.03891 |