Summary of Bellman Diffusion: Generative Modeling As Learning a Linear Operator in the Distribution Space, by Yangming Li et al.
Bellman Diffusion: Generative Modeling as Learning a Linear Operator in the Distribution Space
by Yangming Li, Chieh-Hsin Lai, Carola-Bibiane Schönlieb, Yuki Mitsufuji, Stefano Ermon
First submitted to arxiv on: 2 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel deep generative model framework called Bellman Diffusion is introduced to address the application gap in Markov Decision Processes (MDPs), specifically in distributional Reinforcement Learning (RL). The nonlinearity of modern Deep Generative Models (DGMs) conflicts with the linearity required by the Bellman equation, making conventional histogram-based methods dominant. To overcome this limitation, Bellman Diffusion maintains linearity through gradient and scalar field modeling, ensuring convergence to the target distribution using divergence-based training techniques and a new type of stochastic differential equation (SDE) for sampling. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows how DGMs can be used in MDP applications, enabling advanced decision-making frameworks. A novel framework called Bellman Diffusion is introduced to address the nonlinearity issue, which allows DGMs to work effectively in MDPs. The framework uses gradient and scalar field modeling to maintain linearity, ensuring convergence to the target distribution. |
Keywords
» Artificial intelligence » Diffusion » Generative model » Reinforcement learning
