Just received the good news that our paper Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale by Wu Changye (吴昌烨), Pierre Pudlo, Julien Stoehr and myself, got accepted in Statistics & Computing! This is great in its own, but further concludes a story that started with Changye’s PhD thesis at Paris Dauphine in 2018, with a revision request from Statistics & Computing that stalled with Changye’s departing for industry in Shanghai and eventually resumed thanks to Julien’s massive investment in coding and improving the learning mechanism. It may also conclude my story with Statistics & Computing, where I am supposed to be the historically most prolific author (?), given the move by Springer to a cash-flow model on 01 January, 2027…
Archive for mirror descent
faster HMC by learning
Posted in Books, Kids, Statistics, University life with tags algorithm, conformal Hamiltonian dynamics, eHMC, Hamiltonian Monte Carlo, HMC, leapfrog integrator, mirror descent, No-U-Turn sampler, NUTS, PhD thesis, population Monte Carlo, publication fees, revision, Scholarly Open Access, Shanghai, Springer Nature, Statistics & Computing, tempering, Università Ca' Foscari Venezia on September 23, 2026 by xi'anconnection between tempering & entropic mirror descent
Posted in Books, pictures, Running, Statistics, Travel, University life with tags ABC, Approximate Bayesian computation, chain-driven bicycle, Edward Langley Fardon, entropy, Fisher-Rao geometry, John Kemp Starley, Kenilworth, mirror descent, National Cycle Networks Sustrans, One World ABC Seminar, penny-farthing, Rover Safety Bicycle, sculpture, sculptures, sequential Monte Carlo, SMC, sunrise, tempering, University of Warwick, Warwickshire, Wasserstein distance, webinar on April 30, 2024 by xi'an 
The next One World ABC webinar is this Thursday, the 2nd May, at 9am UK time, with Francesca Crucinio (King’s College London, formerly CREST and even more formerly Warwick) presenting
“A connection between Tempering and Entropic Mirror Descent”.
a joint work with Nicolas Chopin and Anna Korba (both from CREST) whose abstract follows:
This work explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC corresponds to entropic mirror descent applied to the reverse Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be seen as a descent scheme of the KL divergence with respect to the Fisher-Rao geometry, in contrast to Langevin dynamics that perform descent of the KL with respect to the Wasserstein-2 geometry. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and derive adaptive tempering rules that improve over other alternative benchmarks in the literature.
