Research map / Optimization / Nonconvex and smooth optimization
ACCELERATING NONCONVEX LEARNING VIA REPLICA EXCHANGE LANGEVIN DIFFUSION
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add position swapping between low- and high-temperature Langevin particles | Replica exchange Langevin diffusion · Nonconvex optimization | χ²-divergence convergence | Helped |
| Add position swapping between low- and high-temperature Langevin particles | Replica exchange Langevin diffusion · Empirical measures | LDP rate function | Helped |
| Use a higher swapping intensity | Replica exchange Langevin diffusion · Nonconvex optimization | χ²-divergence convergence | Helped |
| Use a higher swapping intensity | Replica exchange Langevin diffusion · Empirical measures | LDP rate function | Helped |
| Swap when the Radon–Nikodym derivative is symmetric across particle positions | Replica exchange Langevin diffusion · Nonconvex optimization | χ²-divergence convergence | No clear effect |
| Swap when the empirical-measure density is symmetric across particle positions | Replica exchange Langevin diffusion · Empirical measures | LDP rate function | No clear effect |
| Use a single-temperature Langevin diffusion instead of replica exchange | Langevin diffusion · Numerical experiments | Performance | Hurt |
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