Research map / Optimization / Nonconvex and smooth optimization
The Randomized Midpoint Method for Log-Concave Sampling
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the randomized midpoint discretization for ULD instead of the prior best HMC collocation method | Log-concave sampling · Strongly log-concave sampling (W₂ error ε·D) | gradient-computation steps: \tilde{O}\left(\kappa^{1.5}/\epsilon\right) -> \tilde{O}\left(\kappa^{7/6}/\epsilon^{1/3}+\kappa/\epsilon^{2/3}\right) | Helped |
| Use stratified random midpoint samples with parallel gradient evaluations | Randomized Midpoint Method for ULD · Strongly log-concave sampling (W₂ error ε·D) | parallel steps: O(\kappa\log\frac{1}{\epsilon}) | Helped |
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