Energy-Weighted Flow Matching for Offline Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909528838111232 |
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| author | Zhang, Shiyuan Zhang, Weitong Gu, Quanquan |
| author_facet | Zhang, Shiyuan Zhang, Weitong Gu, Quanquan |
| contents | This paper investigates energy guidance in generative modeling, where the target distribution is defined as $q(\mathbf x) \propto p(\mathbf x)\exp(-β\mathcal E(\mathbf x))$, with $p(\mathbf x)$ being the data distribution and $\mathcal E(\mathcal x)$ as the energy function. To comply with energy guidance, existing methods often require auxiliary procedures to learn intermediate guidance during the diffusion process. To overcome this limitation, we explore energy-guided flow matching, a generalized form of the diffusion process. We introduce energy-weighted flow matching (EFM), a method that directly learns the energy-guided flow without the need for auxiliary models. Theoretical analysis shows that energy-weighted flow matching accurately captures the guided flow. Additionally, we extend this methodology to energy-weighted diffusion models and apply it to offline reinforcement learning (RL) by proposing the Q-weighted Iterative Policy Optimization (QIPO). Empirically, we demonstrate that the proposed QIPO algorithm improves performance in offline RL tasks. Notably, our algorithm is the first energy-guided diffusion model that operates independently of auxiliary models and the first exact energy-guided flow matching model in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy-Weighted Flow Matching for Offline Reinforcement Learning Zhang, Shiyuan Zhang, Weitong Gu, Quanquan Machine Learning This paper investigates energy guidance in generative modeling, where the target distribution is defined as $q(\mathbf x) \propto p(\mathbf x)\exp(-β\mathcal E(\mathbf x))$, with $p(\mathbf x)$ being the data distribution and $\mathcal E(\mathcal x)$ as the energy function. To comply with energy guidance, existing methods often require auxiliary procedures to learn intermediate guidance during the diffusion process. To overcome this limitation, we explore energy-guided flow matching, a generalized form of the diffusion process. We introduce energy-weighted flow matching (EFM), a method that directly learns the energy-guided flow without the need for auxiliary models. Theoretical analysis shows that energy-weighted flow matching accurately captures the guided flow. Additionally, we extend this methodology to energy-weighted diffusion models and apply it to offline reinforcement learning (RL) by proposing the Q-weighted Iterative Policy Optimization (QIPO). Empirically, we demonstrate that the proposed QIPO algorithm improves performance in offline RL tasks. Notably, our algorithm is the first energy-guided diffusion model that operates independently of auxiliary models and the first exact energy-guided flow matching model in the literature. |
| title | Energy-Weighted Flow Matching for Offline Reinforcement Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.04975 |