Irreversible Monte Carlo algorithms for efficient sampling

Equilibrium systems evolve according to Detailed Balance (DB). This principle guided the development of Monte Carlo sampling techniques, of which the Metropolis–Hastings (MH) algorithm is the famous representative. It is also known that DB is sufficient but not necessary. We construct irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known distribution. Our transformation modifies transition rates keeping the structure of transitions intact. To illustrate the general scheme we design an Irreversible version of Metropolis–Hastings (IMH) and test it on an example of a spin cluster. Standard MH for the model suffers from critical slowdown, while IMH is free from critical slowdown.

Research highlights
► Detailed balance is sufficient but not necessary for MCMC algorithm convergence.
► The generalized balance condition can be satisfied by the introduction of currents.
► Strong reduction of mixing time is achieved in the Ising spin cluster model.
► The algorithm can be applied to other systems.