Research map / Learning theory and algorithms / Sample complexity
Sqrt(d) Dimension Dependence of Langevin Monte Carlo
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use refined mean-square analysis and track the dimension dependence of its constants | LMC · LMC mixing time, 2-Wasserstein | mixing time: \tildeO{\frac{d}{\epsilon}} -> \tildeO{\frac{\sqrt{d}}{\epsilon}} | Helped |
| Require linear growth of the third-order derivative of the potential | LMC · LMC mixing time, 2-Wasserstein | mixing time | Helped |
| Add the Metropolis adjustment | Overdamped Langevin sampling · Mixing time, 2-Wasserstein | mixing time | Mixed |
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