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Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
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In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure. Finally, we apply these results to bound the excess risk optimization error of the associated optimization problem.
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kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients
kTULA achieves a non-asymptotic KL convergence of order lambda^(2-epsilon) for non-log-concave targets with super-linear log-gradients under a Log-Sobolev inequality, improving prior order-lambda KL bounds.
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