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

arXiv 2112.00565 ↗First posted 1 Dec 2021stat.ML cs.LG stat.COcited by 0

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Abstract (arXiv)

In this paper, we consider sampling from a class of distributions with thin tails supported on ℝd 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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 9 of its 26 references that are in the map. First posted on arXiv 1 Dec 2021.

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References · 9

  1. 2014Convex Optimization: Algorithms and Complexitycited by 569
  2. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  3. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  4. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  5. 2017Convergence of Langevin MCMC in KL-divergencecited by 86
  6. 2018Sampling Can Be Faster Than Optimizationcited by 68
  7. 2020Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithmcited by 57
  8. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  9. 2019Dual Space Preconditioning for Gradient Descentcited by 7

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