Feedback mechanism for swap dynamics that captures mixing objectives

Develop a swap-dependent feedback mechanism for parallel tempering Markov Chain Monte Carlo that effectively captures the objective of reducing autocorrelation and improving mixing, suitable for use as a reward or control signal when adaptively selecting temperatures.

Background

Sampler efficiency in parallel tempering is typically assessed via integrated autocorrelation time, but using ACT directly as a feedback signal is impractical during sampling. Common alternatives such as acceptance-rate uniformity or ESJD either focus on swap efficiency without fully reflecting mixing impact or can be computationally burdensome.

The paper proposes the swap mean-distance metric as a proxy, showing strong empirical correlations with ACT. Nonetheless, the authors explicitly note that constructing a feedback mechanism that reliably captures the mixing objective during swapping remains an open challenge, motivating continued investigation into more effective reward designs.