Complexity of randomized algorithms for underdamped Langevin dynamics
dc.contributor.author | Cao, Y | |
dc.contributor.author | Lu, J | |
dc.contributor.author | Wang, L | |
dc.date.accessioned | 2020-07-30T01:20:23Z | |
dc.date.available | 2020-07-30T01:20:23Z | |
dc.date.updated | 2020-07-30T01:20:23Z | |
dc.description.abstract | We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is of order $\Omega(\sqrt{d}, N^{-3/2})$, for solving a family of $d$-dimensional underdamped Langevin dynamics, by any randomized algorithm with only $N$ queries to $\nabla U$, the driving Brownian motion and its weighted integration, respectively. The lower bound we establish matches the upper bound for the randomized midpoint method recently proposed by Shen and Lee [NIPS 2019], in terms of both parameters $N$ and $d$. | |
dc.identifier.uri | ||
dc.publisher | International Press of Boston | |
dc.subject | math.NA | |
dc.subject | math.NA | |
dc.subject | cs.NA | |
dc.subject | math.PR | |
dc.title | Complexity of randomized algorithms for underdamped Langevin dynamics | |
dc.type | Journal article | |
duke.contributor.orcid | Lu, J|0000-0001-6255-5165 | |
duke.contributor.orcid | Wang, L|0000-0002-9130-0505 | |
pubs.organisational-group | Trinity College of Arts & Sciences | |
pubs.organisational-group | Chemistry | |
pubs.organisational-group | Mathematics | |
pubs.organisational-group | Physics | |
pubs.organisational-group | Duke | |
pubs.organisational-group | Student |