Publications [#359229] of Jianfeng Lu

Papers Published

1. Cao, Y; Lu, J; Wang, L, COMPLEXITY OF RANDOMIZED ALGORITHMS FOR UNDERDAMPED LANGEVIN DYNAMICS*, Communications in Mathematical Sciences, vol. 19 no. 7 (January, 2021), pp. 1827-1853, International Press of Boston [doi]
   (last updated on 2026/01/14)

   Abstract:
   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.