Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914068924727296 |
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| author | Srinivasan, Rishikesh Nagaraj, Dheeraj |
| author_facet | Srinivasan, Rishikesh Nagaraj, Dheeraj |
| contents | We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($W_2$), achieving a cubic speedup in dependence on the target accuracy ($ε$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_07614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds Srinivasan, Rishikesh Nagaraj, Dheeraj Probability Machine Learning Statistics Theory We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($W_2$), achieving a cubic speedup in dependence on the target accuracy ($ε$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature. |
| title | Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds |
| topic | Probability Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2506.07614 |