Randomized step sizes make Metropolis–Hastings robust to tuning, study finds
michaelchchoi · x · 2026-09-22
Paper 3 of the JJSD Monte Carlo special issue thread (open access): Grazzi, Livingstone & Riou-Durand study Metropolis–Hastings with randomized step sizes via auxiliary-variable and marginalized constructions. Key results: randomized algorithms inherit weak Poincaré inequalities/spectral gaps from fixed-step counterparts under minimal conditions; the marginalized kernel always beats the auxiliary-variable one in asymptotic variance when implementable; both randomizations make the algorithm robust to tuning, with spectral gaps decaying only polynomially under poor step sizes; randomization often preserves high-dimensional scaling limits while raising optimal acceptance rates for Langevin and Hamiltonian samplers with Exponential or Uniform randomization. Numerical study covers Poisson regression, Neal's funnel and Rosenbrock.
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