COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*
Publication
, Journal Article
Cao, Y; Lu, J; Wang, L
Published in: Communications in Mathematical Sciences
January 1, 2021
We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst L2 strong error is of order (Formula Presented), for solving a family of d-dimensional underdamped Langevin dynamics, by any randomized algorithm with only N queries to rU, 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.
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Published In
Communications in Mathematical Sciences
DOI
EISSN
1945-0796
ISSN
1539-6746
Publication Date
January 1, 2021
Volume
19
Issue
7
Start / End Page
1827 / 1853
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
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Chicago
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MLA
NLM
Cao, Y., Lu, J., & Wang, L. (2021). COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*. Communications in Mathematical Sciences, 19(7), 1827–1853. https://doi.org/10.4310/CMS.2021.v19.n7.a4
Cao, Y., J. Lu, and L. Wang. “COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*.” Communications in Mathematical Sciences 19, no. 7 (January 1, 2021): 1827–53. https://doi.org/10.4310/CMS.2021.v19.n7.a4.
Cao Y, Lu J, Wang L. COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*. Communications in Mathematical Sciences. 2021 Jan 1;19(7):1827–53.
Cao, Y., et al. “COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*.” Communications in Mathematical Sciences, vol. 19, no. 7, Jan. 2021, pp. 1827–53. Scopus, doi:10.4310/CMS.2021.v19.n7.a4.
Cao Y, Lu J, Wang L. COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*. Communications in Mathematical Sciences. 2021 Jan 1;19(7):1827–1853.
Published In
Communications in Mathematical Sciences
DOI
EISSN
1945-0796
ISSN
1539-6746
Publication Date
January 1, 2021
Volume
19
Issue
7
Start / End Page
1827 / 1853
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics