Proximal Algorithms for Accelerated Langevin Dynamics
This addresses the problem of efficient sampling for statisticians and machine learning practitioners, representing a novel method for a known bottleneck rather than an incremental improvement.
The authors tackled the problem of slow convergence in Markov Chain Monte Carlo sampling by developing a novel class of MCMC algorithms based on a stochastized Nesterov scheme, which resulted in superior performance over typical Langevin samplers with better mixing of Markov chains across statistical and image processing models.
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target distribution as its invariant measure. Convergence rates to stationarity under Wasserstein-2 distance are established as well. Metropolis-adjusted and stochastic gradient versions of the proposed Langevin dynamics are also provided. Experimental illustrations show superior performance of the proposed method over typical Langevin samplers for different models in statistics and image processing including better mixing of the resulting Markov chains.