Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms

Francesca R. Crucinio; Alain Durmus; Pablo Jiménez; Gareth O. Roberts

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arXiv · 2301.02446

Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms

Francesca R. Crucinio·Alain Durmus·Pablo Jiménez·Gareth O. Roberts

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Abstract

We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yosida envelope for the target of interest, which depends on a parameter $\lambda$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods.

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Francesca R. Crucinio, Alain Durmus, Pablo Jiménez, Gareth O. Roberts. 2023-01-06. Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms. https://arxiv.org/abs/2301.02446

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