Summary of Soft-constrained Schrodinger Bridge: a Stochastic Control Approach, by Jhanvi Garg et al.
Soft-constrained Schrodinger Bridge: a Stochastic Control Approach
by Jhanvi Garg, Xianyang Zhang, Quan Zhou
First submitted to arxiv on: 4 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Computation (stat.CO)
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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 This paper proposes a novel optimization problem called Soft-Constrained Schrödinger Bridge (SSB), which generalizes the traditional Schrödinger bridge by allowing for a difference between the terminal distribution and target distribution, while penalizing the Kullback-Leibler divergence between them. The authors derive the theoretical solution to SSB, showing that the terminal distribution is a geometric mixture of the target and another distribution. This result is extended to a time series setting and has applications in developing robust generative diffusion models. A score matching-based algorithm for sampling from geometric mixtures is proposed and demonstrated on the MNIST dataset. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to control processes so that they end up with a target distribution, but allows some flexibility by letting the final result differ slightly from the target. The researchers figured out how to solve this problem mathematically and showed it can be applied to time series data. This has potential applications in developing better algorithms for generating fake data that looks real. |
Keywords
* Artificial intelligence * Optimization * Time series
