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arXiv · 2112.00565

On Mixing Times of Metropolized Algorithm With Optimization Step (MAO) : A New Framework

EL Mahdi Khribch·George Deligiannidis·Daniel Paulin
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Abstract

In this paper, we consider sampling from a class of distributions with thin tails supported on $\mathbb{R}^d$ and make two primary contributions. First, we propose a new Metropolized Algorithm With Optimization Step (MAO), which is well suited for such targets. Our algorithm is capable of sampling from distributions where the Metropolis-adjusted Langevin algorithm (MALA) is not converging or lacking in theoretical guarantees. Second, we derive upper bounds on the mixing time of MAO. Our results are supported by simulations on multiple target distributions.

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EL Mahdi Khribch, George Deligiannidis, Daniel Paulin. 2021-12-01. On Mixing Times of Metropolized Algorithm With Optimization Step (MAO) : A New Framework. https://arxiv.org/abs/2112.00565

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