Tamed Stochastic Gradient Hamiltonian Monte Carlo

• URL: http://arxiv.org/abs/2607.14862v1
• Date: Thu, 16 Jul 2026 11:36:00 GMT
• Title: Tamed Stochastic Gradient Hamiltonian Monte Carlo
• Abstract summary: We propose a novel tamed gradient Hamiltonian Monte Carlo (tSGHMC) algorithm for sampling and optimization problems with superlinearly growing gradients.<n>We show that tSGHMC achieves lower root mean square error and expected excess risk across a range of tasks.
• Score: 6.75602425917782
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a novel tamed stochastic gradient Hamiltonian Monte Carlo (tSGHMC) algorithm for sampling and stochastic optimization problems with superlinearly growing stochastic gradients. Under a certain continuity in average condition and a strong convexity condition, we establish a non-asymptotic error bound in Wasserstein-2 distance for tSGHMC with the rate of convergence equal to $1/4$. Then, we derive an upper estimate for the associated expected excess risk, which provides a theoretical guarantee for the performance of tSGHMC. To illustrate the effectiveness of the proposed algorithm, we apply tSGHMC to practical examples, including a newsvendor problem and a Conditional Value-at-Risk minimization problem, using synthetic and real-world datasets. Numerical results support our theoretical findings. Furthermore, we compare tSGHMC with its first-order counterpart, namely, the tamed unadjusted stochastic Langevin algorithm. Simulation results demonstrate that tSGHMC achieves lower root mean square error and expected excess risk across a range of tasks.

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