Summary of Continuous-time Riemannian Sgd and Svrg Flows on Wasserstein Probabilistic Space, by Mingyang Yi et al.
Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Space
by Mingyang Yi, Bohan Wang
First submitted to arxiv on: 24 Jan 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 enriches continuous optimization methods in Wasserstein space by extending gradient flow to stochastic gradient descent (SGD) and variance reduction gradient (SVRG) flows. It leverages the properties of Wasserstein space to construct stochastic differential equations (SDEs) for discrete dynamics, obtaining probability measure flows through Fokker-Planck equations. The convergence rates of these Riemannian stochastic flows are proven, matching results in Euclidean space. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper helps make optimization more efficient by exploring new ways to optimize on a special kind of math problem called the Wasserstein space. This space is important because it’s connected to real-world problems like sampling data. The researchers take existing optimization methods and adapt them for use on this space, making them “stochastic” or random. They show that these adapted methods can be used to solve problems more quickly and accurately than before. |
Keywords
* Artificial intelligence * Optimization * Probability * Stochastic gradient descent
