Determine the practical regime of the work-based Rényi-divergence estimator

Determine whether estimating Rényi divergences through exponentiated-work averages provides practical advantages over direct distribution-based estimation, especially in the intermediate regime where the estimator is both computationally tractable and informative for Monte Carlo simulations and machine learning.

Background

The paper notes that direct estimation of Rényi divergences can require a number of samples scaling with the square root of the alphabet size, whereas the proposed work-based estimator has a cost governed by the work variance rather than the bath-distribution alphabet size.

The estimator is well behaved near equilibrium when work distributions are sharply peaked and bath measurements have no heavy tails, but this is also the regime in which the bath is barely perturbed and the Rényi divergence is small. The authors explicitly identify the intermediate regime, where the estimator would be both tractable and informative, as unresolved.