Summary of Stochastic Optimal Control For Diffusion Bridges in Function Spaces, by Byoungwoo Park et al.
Stochastic Optimal Control for Diffusion Bridges in Function Spaces
by Byoungwoo Park, Jungwon Choi, Sungbin Lim, Juho Lee
First submitted to arxiv on: 31 May 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 The paper presents a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. The authors demonstrate how Doob’s h-transform can be derived from the SOC perspective and expanded to infinite dimensions, overcoming the challenge of lacking closed-form densities in these spaces. They show that solving an optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. Two applications are proposed: learning bridges between two infinite-dimensional distributions and generative models for sampling from an infinite-dimensional distribution. The approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper helps us understand how we can use computers to learn about infinite sets of functions. This is important because many real-world problems involve functions that are not fixed but rather changing over time. The authors show how a technique called stochastic optimal control can be used to learn about these function spaces and create models that can generate new functions based on existing ones. |
Keywords
» Artificial intelligence » Diffusion » Objective function » Probability » Time series
