Forward event-chain Monte Carlo: taming randomness by symmetry exploitation

Since fifty years, the conservation of the equilibrium probability distribution in Markov chain Monte Carlo was ensured by the artificial introduction of the reversibility symmetry (left). During the 2010s, non-reversible Markov chains (right), breaking the reversibility symmetry, were introduced and shown to be faster. We show how they still rely on an artificial local symmetry and how by replacing this artificial symmetry into a real one (invariance by rotation aroung the energy gradient) we obtain a dramatic acceleration (right). This generalized non-reversible MCMC is called the Forward event-chain Monte Carlo method.