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Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
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abstract
We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution $\pi$ on $\mathbb{R}^{d}$, showing that HMC mixes quickly in this setting. One of our main results is a dimension-free bound on the mixing of an "ideal" HMC chain, which is used to show that the usual leapfrog implementation of HMC can sample from $\pi$ using only $\mathcal{O}(d^{\frac{1}{4}})$ gradient evaluations. This dependence on dimension is sharp, and our results significantly extend and improve previous quantitative bounds on the mixing of HMC.
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Cited by 1 Pith paper
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High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm
A third-order Langevin MCMC algorithm is proven to sample from smooth log-concave distributions in O(d^(1/4)/epsilon^(1/2)) iterations for generalized linear model potentials, improving on the earlier d^(1/3) barrier.
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