Optimal temperature ladder selection in parallel tempering MCMC

Determine the optimal selection of chain temperatures T = {T1 < T2 < ... < TM} with T1 = 1 for parallel tempering Markov Chain Monte Carlo that maximizes sampler efficiency for a given target distribution, recognizing that the temperatures enabling effective crossings of entropic barriers and phase-transition regions depend strongly on distribution-specific features.

Background

Parallel tempering augments standard MCMC with multiple replicas at different temperatures that periodically swap states to improve exploration of multimodal landscapes. The efficiency of this method critically depends on the choice of the temperature ladder. While geometric spacing is optimal for Gaussian targets and uniform acceptance-rate schemes are widely used, temperature configurations that best facilitate barrier crossing and information flow vary substantially across target distributions.

This paper frames temperature selection as a reinforcement learning problem, proposing a policy-gradient approach to adapt temperatures using reward functions that aim to reduce autocorrelation. Despite these advances, identifying a principled and generally optimal temperature ladder remains explicitly unresolved in the literature.